Congratulations on pretty much everything about this!
You may be able to find some kind of employee resource group to reach out to. You could ask if there's any sort of LGBT group, and ask them the actual questions. That does mean sort of vaguely outing yourself, but then you can save the trans-specific questions for the folks you hopefully get referred to. If the company is too small there may be no such group (or not a formal enough one for your contacts to be aware of), but then it's hard to generalize about culture anyways. You might also be able to work toward good contacts for this by asking about things like organized volunteering.
(I know where I work this would be incredibly helpful - there's a great group, and there'd be plenty of people willing to talk to a prospective new employee.)
Failing that, my next inclination would be to try to get a one on one chat with your hiring manager (or maybe someone from the team you'd join), and try to gauge their attitudes. If it's a sufficiently friendly, social chat, you don't necessarily have to out yourself for that; you may be able to work your way into it, e.g. by mentioning a current event, a volunteering experience, or a trans friend or someone you admire. If it's in person and you're comfortable with it at this point, you could also just present a bit feminine and try to gauge reactions.
This is definitely more difficult, of course, because you ideally want to get a lot of information out of gauging attitudes. If it seems positive initially , you may want to progress to more specific questions and try to pin things down. The difference between token and genuine support is generally quite obvious - the former will come with few specifics and often some non sequiturs or flat out mistakes - but the more you ask the more you know! Still, I would try to avoid giving too much personal detail, because while it may be obvious down the line anyway, it's nice to retain that option to let things remain unsaid. For example, I'd ask about gender neutral restrooms, but not say anything about what restrooms I intend to use at what point in my process.
You may also be able to ask about some official policies without revealing anything, for example by asking to see the employee handbook, or health insurance policies. This unfortunately will only be able to tell you things at a very impersonal level, though; there's a big difference between policies on paper and day-to-day behavior.
If it's sufficiently feasible, you could try to do all of the above: learn about the overall company, others' experiences there, and the team you're joining. In the end you'll care about it all: the overall company can provide structural support (restrooms, insurance) while the people you see daily are the ones who can have the most direct impact. And there can be a lot of variation across a company, so an overall good place can have both welcoming and unwelcoming teams.
Overall, in terms of whether to ask, my personal advice would be to err on the side of caution and try to get whatever information you can up front. If the people you'll be working with are kind and understanding about these things, it can make your life immensely better, and if they're the opposite, it can make you miserable enough to leave your job. It is absolutely worth finding a good fit. My team has been solid and my manager has been incredible (thank you thank you!) and I can't imagine doing everything I've done without that support. (You could try to accomplish this by just promising yourself that you'll just leave if it's not working for you, but that sounds much more difficult to me both in terms of emotional burden and job-hunting.)
Ideally I would do all of this once you actually have an offer. Partially that's just to avoid spending time and energy before you know, but it's also about protecting yourself against possible bias from whoever you're talking to. Of course if the whole company has bad attitudes then missing an offer would be no big loss, but it'd be a shame to miss out because of one person.