Unlike the other review, I have been fairly impressed with this card. The key to using Stoneship Chart Room effectively isn't in its upside – the card's abilities are marginal at best. Rather, unusually for Netrunner cards, Stoneship Chart Room has an almost complete lack of downsides (assuming that you're playing Shaper already – if you're considering importing this, consider Build Script or Deuces Wild instead, or maybe Blueberry!™ Diesel if in Criminal).
One thing to note is that the second ability here is really marginal, but it isn't what the card is really about. Netrunner decks often get into situations where they're very slightly short of something they need in order to win the game, so the second ability does have its uses – if you're one Endurance or Propeller or Revolver counter short of being able to steal the critical agenda, then sure, you'd use it and go do your run. But this has very little impact on the card's strength, which is nearly all in the primary ability, so the rest of the review is going to focus on that.
There are two cards I want to look at as almost direct comparisons for Stoneship Chart Room (when you're planning to use its first ability): Diesel and Build Script. Each of these is "one basic action" better than Stoneship Chart Room is (with Diesel drawing an extra card and Build Script giving you an extra credit). They both have issues of their own, though.
First off, Diesel. This is a widely played card, but it isn't an auto-include, and the reason is that it's somewhat clunky. When you play it, it draws you three cards, which is great; but now your hand is three cards larger, and if it was already fairly large, you're going to need to play some of those cards right away to avoid having to discard some to hand size (and lose most of the benefit of playing Diesel in the first place). So Diesel is a card that functions best in decks which can dump their hand onto the board easily and need help refilling it. That's only a minority of decks, though – it's rare for decks to be full of cheap cards, so installing things to get them out of your hand comes at a credit cost, and it's hard to get enough credits early to clear things from your hand at enough of a rate to use Diesel at full efficiency. Additionally, many decks want to play situational events, which have to be held in hand until they're ready – you can't just install them, they're going to count against the hand size limit no matter what, and should six of them end up in hand at once, you're going to have to discard some. Diesel also has timing issues to some extent; if you're holding back critical cards, you have to play it early in a turn because you can't keep both your critical cards, and the draws off Diesel, in hand simultaneously during the Corp turn.
Diesel is also useful for digging through your deck in a hurry to find some specific card (e.g. to set up a combo), but at the cost of having to uselessly discard some of your deck (and VRcation would be better if this were your main reason to play the card). Many decks can't afford to be throwing cards away.
Meanwhile, Build Script draws only two cards rather than three, which is much easier to deal with in terms of hand size issues; normally, you can just leave a Build Script in your hand until the next time you would click to draw a card, and then play the Build Script to, effectively, replace the Build Script with a random card at the same time as you draw, with a 1 bonus thrown in. In other words, it's as though the Build Script isn't in your deck at all (and you gained 1 out of nowhere), because it turns itself into another card in your deck; so this effectively lets you cheat on the minimum deck sizes, making your deck just that little bit more efficient.
There's still a bit of hand size pressure when doing this, though (the Build Script itself is a situational event, which needs to be held in your grip alongside the other situational cards which might be in your deck), but that downside isn't huge, and Build Script goes a long way towards, effectively, making your deck 3 cards smaller and thus a lot more efficient. Its real downside, and the reason that it isn't played much, is that dot of universal influence; paying a point of influence normally isn't worth it for a gain this marginal.
In Shaper, Stoneship Chart Room is like a Build Script that gives up 1 to avoid spending the influence dot, or a Diesel that gives up a card in exchange for completely avoiding the hand size issues. Either of those on their own would be enough to, in effect, play a 42 (or 37) card deck. You also don't face any problems with timing, nor with holding enough cards in your hand at once; being a resource, Stoneship Chart Room can be played equally viably on any of the four clicks of your turn, and will peacefully wait in your rig until the correct moment to use it. So unlike Diesel or Build Script, Stoneship Chart Room isn't even counting towards your maximum hand size.
Another key advantage of Stoneship Chart Room is that the value of Runner clicks varies a lot over short timescales. It's fairly common to be in a situation where a click is mostly useless. Say you've come to the last click of your turn, already have a full hand, and need to avoid playing something because they're situational cards that don't make sense in this situation, or would put your credit count dangerously low. Depending on what Corp deck you're up against, running last click may be a very bad idea, and so you may be forced into clicking for a credit, which is mostly a waste of a click. Stoneship Chart Room has a fairly even value regardless of when you play it, so its install cost is effectively slightly lower than normal; the card costs but it isn't any , it's specifically the that would otherwise be least useful (which in most decks, is effectively 1). So although the card looks entirely economically neutral, there is in practice a little economy being gained from playing it; you're spending 1 card, plus an unusually useless click, to gain 2 cards, which is about equal in value to clicklessly and cardlessly trading 1 for 1 card. That's a very small gain, but it's a positive gain (e.g. the ability to do that repeatedly is the primary reason why people play Hoshiko, who is frequently one of the strongest runners), and you've effectively given up nothing at all to do that (other than shrinking your deck very slightly).
Stoneship Chart Room does have one disadvantage, but it's pretty small, and the reduction in effective deck size is probably worth more: prior to the point at which you'd do your first click-for-draw of the game, it's taking up space which could have been a more impactful card. Most decks will click to draw very early (usually on turn 1), so this doesn't matter much, but it does have an impact on your mulligan decision; if there's a Stoneship Chart Room in your first potential opening hand, it's kind-of like having one card hidden when you're deciding whether to mulligan that hand or not.
(Another marginal disadvantage – if Stoneship Chart Room is the second-last card in your deck, it'll costing you an extra click or card draw ability to get at the last card, without the Chart Room itself being usable. The odds of the cards ending up in that specific order are fairly low, though, and the situation only matters if you end up going through your entire deck, so this downside will hardly ever come up. Note that having a Stoneship Chart Room as the last card in your deck is not a problem, as that gives you the effective reduction in deck size via another mechanism, and even gives you a blank card at the end to act as a hitpoint, so it's position 44 specifically that causes issues.)
So far, this review has been considering Stoneship Chart Room from the point of view of "this card has only a slight upside, but the downside is basically nonexistent (even taking into account the deck slots you're using to play it), so if you're in Shaper, you may as well play it". But we're in Shaper, the faction of complex card interactions and weird jank combos, so unsurprisingly, there are going to be situations where the card suddenly starts pulling well above its weight in terms of the amount of upside it gives you.
The first combo I want to highlight, because it's the first one I noticed, is with Lat: Ethical Freelancer. Lat a) is most commonly used with weird combo decks that require holding lots of specific cards in hand until you unleash them all on the same turn, thus normally can't play Diesel effectively, and b) has an ability that cares a lot about the exact number of cards in your hand at the moment your turn ends. Stoneship Chart Room lets you cheat on Lat's trigger timing, because you have a choice about when to use its trash ability: if having a low number of cards in hand would be beneficial that turn, you can let your turn end and then pop the Chart Room; but if having a high number of cards would be beneficial, you can pop the Chart Room before ending your turn. So it's basically giving you two chances to hit Lat's magic card count in a single turn. Successfully triggering Lat is worth a card, so if it helps you out with Lat's trigger, your Stoneship Chart Room is basically worth three cards rather than two, making it into a true Diesel, but without any of the downsides.
Even if you aren't playing Lat, though, Stoneship Chart Room has another ability: it lets you be above your maximum hand size during the Corp's turn, in much the same way that Sports Hopper used to. Most decks have a maximum hand size of 5; ending your turn with 5 cards in hand, then popping Stoneship Chart Room, can get that up to 7. And 7 cards in hand is a very critical number in today's metagame, because it lets you survive BOOM!. If you fear you're up against a BOOM! deck, you can use your Chart Room as a tech card, rather than a deck-thinner; just install it, and leave it in place until you get tagged on the Corp turn, and pop it at that point. Although you'll probably end up getting BOOM!ed and losing 7 cards, at least you didn't lose the game, and you'll have some chance to recover (depending on how much the Corp invested into their combo, you may be able to recover faster than they can). There are better tech cards against BOOM! (e.g. Jarogniew Mercs – you can install it and immediately clear the tag), but they're mostly dead in the majority of matchups. Stoneship Chart Room has the advantage of being a tech card in the matchup that needs it, whilst still being (marginally) beneficial in matchups where flatline combos are completely irrelevant.
Along similar lines, you can use Stoneship Chart Room to have extra cards in your hand during your own turn, e.g. to steal a City Works Project or Obokata Protocol. It also often allows digging for a combo to happen one turn sooner (this is technically a side effect of the way it replaces "your most useless click" with a card draw on a future turn, but this implication is non-obvious and thus worth pointing out).
Finally, nothing's forcing you to use the abilities on Stoneship Chart Room; you can treat it as a blank 0-cost resource if you'd prefer. This is a side benefit of the card, but it's still relevant if your deck is running, e.g., Dummy Box or Aesop's Pawnshop (or in older formats, Hayley Kaplan: Universal Scholar).
Conclusions: this card is not worth spending even one influence dot on, but it should quite possibly be an auto-include if you're playing Shaper; unlike almost every other card in the game (where you're paying something if you put it in your deck), with this card you are in effect paying nothing at all to include it, and thus it doesn't matter how small the (fairly small) upside is. The primary upside is that you're playing with an effectively smaller deck size, meaning that the best cards in your deck are more likely to come up over the course of the game (and yet if you're up against a grinder deck, you can choose to play it like a blank 0-cost resource instead, so you can even dodge the main downside of shrinking your deck). It helps smooth your economy slightly by allowing you to postpone a card-drawn-by-click to a later turn, meaning that you get a bit more use out of otherwise low-value clicks; this is pretty minor but can speed up combo decks by a turn sometimes. It'll also serve as a tech card in some matchups, whilst not costing anything in others; and you can use it as part of combos, especially when playing Lat (or just sell it to Aesop if 3 are more important than 2 cards and you have nothing else to sell). There are some very slight downsides, but they're much smaller than the downsides of other comparable cards, so there's very little reason not to run this.
The main reason you wouldn't run this in Shaper would be if your deck never or rarely spends one click to draw one card (e.g. you're running Professional Contacts or Verbal Plasticity, thus your card-drawing clicks have useful side effects). That can certainly happen, but it's likely to be only a minority of Shaper decks.