Plain Waydroid might work depending on the exact application you're using. Try that first because it's pretty seamless and has good performance (as Android processes run directly on the OS).

I used it for three years before giving up and getting a used phone (for other reasons). My banking application detected all other emulators, but not Waydroid.

Alternative mobile OSes may work for banking apps, it's hit or miss. For example, SailfishOS (perhaps the only viable Linux distribution on phones, a successor of Nokia N770-N9) comes with an Android emulation layer if you purchase the license. Many banking apps work fine there.

Frankly, I find the current situation really frustrating from a security perspective and also because it has created a duopoly that is impossible to escape. Some banks offer SMS as 2FA (insecure, very susceptible to SIM cloning). Others offer push notifications inside apps (iOS or Android with Google Play services) which is not really a second factor, and pushes you to either Apple or Google. I wish hardware keys were more widespread and/or ChipTAN was still an option.