I installed Bitwarden from F-Droid, but I happened to notice yesterday that Bitwarden was in my list of apps with updates available from Play Store, even though I installed it via F-Droid. Why would that be?
I know this is a better question for the Bitwarden forums, but I don’t have enough street cred there to make a post.
Not manifest, their signature must match. Usually F-Droid apps have their own signature but they also support providing your own signature precisely for compatibility with other stores.