[strcat]

You can bypass Play Store restrictions on app installs by using Aurora Store. There's a high chance your banking app can be used but it may require toggling the per-app exploit protection compatibility mode. Most banking apps work on GrapheneOS. X is one of extremely few apps disallowing using a non-Google-certified OS but it only partially disallows it in their store listing which can be worked around and for regular password login. Login is still possible to X via a passkey or Google login. X should stop doing that but they're quite understaffed and did this as a misguided anti-spam measure.

[linux_modder]

Aurora store is a horrible placeabo. Not only is it using other folks anonymized accounts, which violates several privacy laws internationally it also still has the Google libraries in their apks like everything else. You are not gaining any privacy or security using Aurora Store or F Droid for that matter but are indeed opening up more attack surface in the supply chain that ends at your device.

[strcat]

GrapheneOS strongly recommends against F-Droid because it has major security deficiencies and adds an unnecessary middleman. Our recommendation is using developer builds of apps. F-Droid doesn't review the code for app updates but rather automatically fetches and builds it. They make questionable downstream changes introducing security vulnerabilities. The Accrescent app store provides developer builds of apps signed by the developers for everything included which can be verified. Play Store provides developer builds but only a subset of older apps are still signed by developers since they phased it out and heavily recommend switching to Play Signing.

Aurora Store is not recommended by GrapheneOS in general. Our recommendation is to use the sandboxed Play Store for installing apps when using sandboxed Google Play in a profile. We recommend only using Aurora Store for bypassing restrictions set by app developers on where their apps can be installed. That's what was said above. It would be better if the Play Store didn't do this.

Contrary to what you're saying, Android apps do not include Google Play libraries by default. They're only included if developers explicitly go out of the way to include them in order to use Google service APIs. Android SDK, etc. is open source as part of AOSP and both the OS and AndroidX libraries are open source too. The proprietary Play libraries are clearly marked as such via being in the GMS namespace.