It’s really difficult to give advice for this situation, but probably I think the most important thing is to maintain open conversation and a good relationship, however it is that things evolve. That way you’ll have more chance to be able to understand how she’s thinking, and how best you might be able to help.
I’d also say don’t assume she thinks in a particular way, based on stereotypes about transgender people. It can be unhelpful to think there is a “gender ideology”, as in reality transgender people think lots of different things.
She’s young and probably will repeat things she has heard that other people think, and will quite likely not have fully developed her own thinking. Keeping open communication will help you help her to develop her own thinking, and you’ll be able to challenge her thinking. You’ll also be able to help her see there are many different ways in which people cope with gender incongruence.
She will probably have a mixture of thoughts both that she is a woman and a man, and maybe nonbinary, even if it’s possible she might say she just thinks she’s a man. If you can help her process those thoughts before she leaps into body modification, she’ll be less likely to get into a situation where she has made changes that can’t be reversed, which she subsequently thinks were the wrong choice.
When trying to understand the issues, don’t listen to only one source (like only here for instance). Listen to what lots of different people say; that way you’ll build deeper knowledge.
If she has autistic / adhd traits she might get hyper focused on something, and you may be able to help her notice that, etc.
You can google what happens in these assessments, but unless there is something glaringly unusual, she’ll likely get a provisional diagnosis.
“I thought that trans people usually show how different they are from their assigned at birth gender...it's obvious, surely?”
Not necessarily. Some people believe that there are people who are really trans, and people who aren’t. A better way of thinking about it, I would suggest, is that the reasons people identify as another gender, transition, alter their bodies, etc, are complex multi-factorial and different for every person. Every person is different.
It’s not likely to be easy, but I wish you all good luck navigating it all!