So you are stuck in the walled garden. Alternatively, you could find a bank not forcing the duopoly on you. Worked for me.
I don't particularly care for the messing around. I'm of an age now where I've done that and prefer to spend my time not working around self-imposed tech issues.
Also, good luck finding a bank in the UK that can support that (without messing around with desktop web instead on mobile instead of the app).
Monzo in UK is fine with rooted and no Google Play. No idea how it would fare inside Waydroid though.
It it's fine with rooted and no Google Play, that would usually mean it will be fine with Waydroid too.