Uphill1945 Hi there! Welcome, and thank you for taking an interest in GrapheneOS.
GrapheneOS is a production quality OS. Great care is given to ensure that usablity is the best that it can be, while maintaining AOSP security to its fullest extent and then expanding on that substantially.
Now, let's get to the nitty gritty:
GrapheneOS allows you to use Google Play Services in a way where they don't get any special treatment/privileges over the OS like they would do on Stock OS or most other operating systems with Google apps.
There's a compatibility layer that teaches these apps how to work within the bounds of the regular app sandbox. To put it simply, play services on GrapheneOS gets zero additional access compared to any other app you install.
You can read about Sandboxed Google Play here:
https://grapheneos.org/features#sandboxed-google-play
On top of that, compatibility is near-perfect. Sandboxed Google Play and toggles to relax hardening for problematic apps (such as the exploit protection compatibility mode toggle for apps that crash due to having memory corruption bugs) make it so you'll be able run most apps smoothly.
For the most part, if an app doesn't work on GrapheneOS, it's for a very specific, and well-documented reason.
On banking apps specifically, this is what the documentation has to say:
https://grapheneos.org/usage#banking-apps
Basically, apps will work unless they require a certified Android OS. In that case, GrapheneOS can't really do anything. It could implement temporary hacky solution to bypass these checks for now, but all sorts of hacks like that will stop working eventually, when things move to more strict measures that can't be bypassed by software.
By the way, there is a way for app developers to whitelist GrapheneOS while blacklisting other non-certified Android operating systems. It's just a matter of developers caring enough to allow GrapheneOS, something that I think we may eventually see in the future. Here's GrapheneOS' guide on how developers can implement this for their app:
https://grapheneos.org/articles/attestation-compatibility-guide
There is a community effort to document banking apps specifically, so you can check to see if your banking app works without any issues. This list of course not exhaustive, but it's a good starting point:
https://privsec.dev/posts/android/banking-applications-compatibility-with-grapheneos/
You also specifically mentioned NFC payments. Gpay doesn't work for the reasons above (it currently requires a certified Android OS). They could of course whitelist GrapheneOS or change their overall approach. There's nothing in GrapheneOS that's fundamentally incompatible with that.
In fact, there are other contactless payment implementations that work because they don't check for certified Android OSes.
In conclusion, I would say that GrapheneOS is a production quality OS, and random things don't just "break". Everything works, and if there's a bug that's unique to GrapheneOS, it's usually fixed impressively quickly. Beyond that, everything that doesn't work is well documented and known, and it's a case of app developers budging, and not because GrapheneOS is buggy or in any way fundamentally incompatible with them.
If you have any further questions, feel free to ask! I hope that covers your initial inquiries.