Sucks to suck.
If a service is sub-par in the browser I don't use it. Be ThE cHaNgE yOu WaNt To SeE. I hate that sentence but it kinda applies here.
I have tried for years but it just doesn't make a difference if enough people in the world don't care loudly enough.
Banks are relying on Play Integrity protection as well as SMS-based 2FA, neither of which are both safe and private.
Unless you have friends, of course, and want to keep in touch. (Not a problem for me).
browser based applications can still gain access to this data, using very similar workflows. E.g. a weather app rendered on a browser is still going to request your location, and can fingerprint that browser to build a user profile. I'm not sure your solution is a solution at all.