I have noticed this issue happens every time I get a new phone and usually I tinker with it enough for it to go away. Since swapping to my Pixel 6 Pro, I can't seem to fix it.
With that background, here's the situation. I use Amazon synchronization and have two factor authentication enabled and can get things synching fine...for a while. After a few days, the syncing seems to just stop. No prompt for logging in, no prompts for logging back in, etc. I have "trust this browser" enabled with 2FA for everything as well. Sometimes, I can login into the browser in the Deliveries app and it seems to go away. But then sometimes, the only way to fix it is to completely remove my Amazon synchronization and re-add it. Usually after a couple of tries it works again. And then a few days later the cycle repeats once again.
During troubleshooting, I usually clear storage/cache/uninstall the app, etc. I do also use my Google account to sync to the Deliveries website as well, just to give some additional info on this too.