But Google is likely trying this dark pattern to sway people away from F-Droid or alt stores by making users uninstall these apps and install it from the Google Play Store.
No, it's the security measure. Anyone can use existing package ID. If the user installs a different app with the same package ID as the other, that new app just overwrites the old app and will have access to the sensitive data of it.
F-Droid apps are built and signed by the people at F-Droid. Apps from Google Play and GitHub are built and signed by the developers themselves. You can update Google Play apps from GitHub and vice versa. That's why I use Obtainium over F-Droid.