Belmarniss is an exceptional young woman. Among other things, she is exceptionally Good (i.e. prosocial). Tanya knew this before the alignment check, obviously.
Belmarniss correctly deduced that you should not enslave people, or kill or torture people, or kill babies (??). Despite growing up in a society where all those things are routine and unremarkable. That's very unusual. Tanya doesn't know anything about drow psychology or sociology, but it's obviously unusual in the sense that the rest of the drow population isn't like that. There's no enclave of nice prosocial drow living on the surface or in a separate underground city, or Belmarniss would have gone there. Granted, she was raised by her mother who seems to share her views, but that just pushes the question back a step.
If Tanya was reborn a drow, she too would want to leave. But would she refrain from harming others in the meantime? From participating in society in the way that was expected and encouraged and rewarded? If she didn't know it would damn her, or if she mistakenly believed she was damned no matter what she did?
Perhaps. But that is because she has lived in two functional societies. She'd know there was something to hope for, when she left. She could look at Taldor and know that it was vastly better than the drow and yet not good enough. She could plan for the long term, if the cost was merely annoying her grandmother or not having as many helping hands around the house. Because she knows what civilization is. She has an enormous tailwind propping her up. A platform from which to judge other cultures and to find them wanting.
If Tanya had been born as a drow for the first time? Well, the concept of 'the same person' might be meaningless if you regress them to an infant. But someone with Tanya's qualities brought up a as drow would simply be a model drow. That much is obvious. Tanya's innate qualities - as opposed to the ones she has cultivated - are learning the rules of the game and playing them to her benefit. By the time she learned there was another world upstairs that was meaningfully different, maybe read books describing the virtues of cooperation, she'd be too enmeshed in local society to leave it. And, of course, she'd be Evil.