Dumdum
I recently changed my Google account for the Play Store: most if not all installed apps were not shown under the apps management with the new account.
To make them appear again in the list, I have to search them in the store, as I would for any new app, then update them (possible only as long as there’s a new version). So, as long as the app has not been updated, it won’t appear in the list.
The funny thing is that when I can update them, the Play Store warns me that the app has not been installed via the Play Store, which doesn’t make sense.
So I would say it’s more part of the quirks of the Play Store than a story of IDs or signatures discrepancies, most of the time.