bookreader you could be harassed to update, even though no updates are available
I think notifications for Play Store updates systematically mean that the Play Store is able to update to a newer version than the Apps repo. The Play Store is pretty much always ahead of the Apps repo and is the recommended way to update.
bookreader those newer versions may not have been tested with grapheneos's compatibility layer.
By default, the Play Store can only update to versions that have been tested and are approved through gmsCompatConfig. Now, ticking the boxes in
Apps > sandboxed Google Play > top right corner > Configure Play Store updates does mean that Play Store will update to untested versions.