The F-Droid site and app are intended for the Open Source world, but since they allowed the addition of custom repositories in the app, it can also be used for many other projects.
https://f-droid.org/wiki/page/Known_Repositories

They even made a convenient way to create your own repos with support for QR codes.
https://f-droid.org/en/repomaker/

Currently anyone can just make use of it, but I suggest a consolidated itch repo.
At a point you have an itch app you could base the delivery system on theirs and simply use the existing repo.

The F-Droid categories should cover all the types of downloads here.
They also have a way of labelling what they call "anti-features", such as containing advertising, using tracking, needing to access a 3rd party account, or needing extra payment to actually use. https://f-droid.org/en/docs/Anti-Features 
Some of these could also relate to downloads available here, so may be worth following their lead.

There is lots of help and info for developers available here https://f-droid.org/en/docs/