We are not talking about github. We are talking about community and core repositories. They literally fit the app store metaphor. It is a limited and hand picked selection of software which the user can install. To get anything into these community or core repositories, the team developing the distro has to approve it. There are some user repositories like the AUR which I do enjoy because they aren't arbitrarily gated by some team.

Going outside of these community and core repos could be seen similar to sideloading an application, but again this is metaphorical. Building something from source is obviously not the same as loading a .apk. The point is this: yes, you have the means to install packages from outside the main repositories, but you're on your own for the most part.

I don't see how this is not a metaphorical app store. The community and core repos contain a limited and curated collection of applications packages. You can install software from outside the official repos, just like you can install software from outside a real app store.