They can, but they'd need to run their own repository.

F-Droid makes it easy to add other repos.

https://f-droid.org/tutorials/create-repo/

https://f-droid.org/tutorials/add-repo/

even if this was true, you can make the app fully oss but most of the main logic would be handled by the server

Why are we even discussing F-Droid here? The topic at hand is whether Google has a monopoly on the Android app market, not whether anyone can put their app on F-Droid, and there are plenty of alternative app stores besides F-Droid.

Why is it a monopoly? Can't you install other app store?

Sorry if that was unclear, I meant that they don't. I'm just confused as to why we're talking about F-Droid specifically.