Then you would want to be able to run Android apps surely? IOS apps are hyper-focused on a limited set of specific hardware produced by a single vendor. Not to mention that Apple sucks to develop for without actually having Apple hardware and Apple operating systems available.
Whatever adware Google is shovelling isn't part of the app your bank provides, so it wouldn't be an issue in the wine-like layer you want. But as other commenters point out, lots of banking apps don't like running in an emulated device.
If you want to use a banking app without Google or Apple dominating your device, look at something which defangs Android like GrapheneOS or LineageOS.
Android apps work quite well already using waydroid. Unfortunate thing about some banking apps is how they go out of their way not to run without play services and safetynet.
Many online applications are increasingly available only as native apps for the iOS/Android systems. Even governments are guilty of this.
Without the ability to run my banking app or do basic interactions with postal services and government institutions, using a Linux phone is a no-go.