You are conflating tools (apt, brew, pip) with stores (Play Store, Appstore, F-Droid).
Android already has the ability to allow a tool to install from different sources (this is how F-droid functions, however only from their own single source).
F-Droid is actually both a tool as well as a repository (which is the one that's included by default in F-Droid the tool). You can add additional repositories to F-Droid the tool.
Android already has the ability to allow a tool to install from different sources (this is how F-droid functions, however only from their own single source).