Hello!
In a nutshell play integrity is used to check whether or not the operating system the app is running on is certified by Google. Now it's advertised as a security feature however that take quickly falls apart as evident by the fact that GrapheneOS isn't and cannot be certified.
As for what you can try, make sure you're logged in in the play store. You can also to block play integrity requests altogether in the app info page, but this will only work if the implementation is broken and they accept no result as a valid outcome.
Beyond that you need to let the app developers know the app is broken for you. Please share the attestation compatibility guide with them, they can use this to whitelist GrapheneOS. If you are looking for a sample template when reaching out, here you go. It's for banking apps but some slight adjustments will make it suitable for government apps and the likes too.