android-translation-layer (ATL) is a Wine-like approach to run Android applications on Linux. Rather than running an Android container like for example Waydroid does this instead implements the Android API. Note that right now it's very much work in progress and almost no app will work yet, but the fact that they have apps like Newpipe and WhatsApp running already is very promising!
Depends on the bank, I've been a customer at four different banks over the last few years, all their apps worked flawlessly without Play Services or microg installed. One just gave a warning.