They have terrible support for banking apps and any app that needs play integrity
You are badly informed.
GrapheneOS has full support for Play Integrity[0].
[0]: https://grapheneos.org/articles/attestation-compatibility-gu...
Does/do your bank/s absolutely always require you to use an app? Is there a desktop/website that you can use? Do they have a brick and mortar location?
Then keep Google crapphone for banking purposes in your drawer, like auth scratch code cards in the past. I don't get that idea of carrying device with bank access in your pocket constantly. Moreover, at least in EU, there is more and more banks which publish their apps in non Google app stores too.
I've had multiple apps attempt to use Play Integrity on my GrapheneOS phone(it tells you when they try), and then just work anyway. Not sure why.
Then don't use those apps. I know it's easier said than done sometimes, but freedom is more important than convenience.
All Swedish banking apps work without issue and many apps that use play integrity works well regardless. It's just some apps that use play integrity that in a certain way that doesn't work.
"Terrible" is incorrect. Yes quite a few don't work but many many do . See:
https://privsec.dev/posts/android/banking-applications-compa...
And what kind of support do you think a Linux phone will have? While also having trash tier security. I don’t see that as an issue (for Americans at least since most banks here don’t use NFC/wallets in their apps), just use the web browser to access your bank.
Also GrapheneOS has in my experience decent banking app support outside of a handful of apps (including, ironically, my main bank which disabled GrapheneOS support a week or two ago). There is a maintained list of working apps that you can see for yourself: https://privsec.dev/posts/android/banking-applications-compa...