Accrescent is a very nice alternative to the Play Store, with a slightly different set of values than F-Droid. They prioritise security and privacy over open code and toolchains (but the project itself is 100% FOSS).

Publishers sign up to the store, then simply upload their pre-built APKs using their signing key (so no need to bundle Qt for a build, like with F-Droid).

If you are looking for an alternative de-googled app store, this would be an easier approach!