I really like !infinitynikki@discuss.tchncs.de, which is available on Android and has controller support. High quality open world game with platforming aimed at women, and I’m really not used to seeing “high quality” and “aimed at women” together in gaming spaces as a woman who played a lot of low-quality girly games on the Nintendo DS back in the day. Warning that it is a gacha game. You can progress without being pressured to spend money, I certainly did not feel pressured to spend and still cleared endgame content, but you can spend money to speed up time-gated things and, of course, for pulls for outfits (it is a dress-up game). So if she is susceptible to those monetization strategies or morally opposed, no go.

I wish I had more recommendations but I am neither an Android user nor a controller user, so this is the only one I know that hits both requirements. I can look at the Google Play store but I have no idea how to tell from there if a game has controller support or not.