It seems like it would be trivial for a user to login to the app acquired from a different store to be able to display a "welcome back" or even something along the lines of a "restore purchases" type of thing.
This can't be reinventing the wheel kind of a thing.
The only way a developer would know a person is an existing user is if they have a user sign up process inside the app itself.
It is doable, the main issues is: 1. Getting users to redownload the app from the Play store 2. Maintaining this registration transfer mechanism
Shattered Pixel Dungeon was a good example of me paying on one platform, and then applying the upgrade to the free app after downloading on another.
This isn't any different from a user switching to a new device and having to download apps again. Not everyone restores from backup and prefers clean installs. Downloading an app again should not be the point of friction