I could reproduce the error on another phone which had already logged into play store. On this phone I got an error message before being redirected to Play Store "Something went wrong, Check that Google Play is enabled on your device and that you're using aun up-to-date version before opening this app. If the problem persists try reinstalling the app."
Of course I do have the newest version and I tried several times reinstalling the app on two phones without success.
After being redirected do Play Store and logging in the app starts working again but I have to re-register using the mobile phone. This registration hangs after entering the sms security code without error message.
I will contact the devs but I do not have much hope. GrapheneOS is too small a market to being paid attention to.