Is there any way to download Fedilab for free outside of the F-Droid repository? I know they have the code on Codeberg but I could not find an APK file on there
They also host their own f-droid repo if you want one built by the developers and not f-droid. https://fdroid.fedilab.app/repo/
Why not download the APK from F-Droid?
F-Droid already acts like CI and builds the app for the developer, it’s as close to an APK from the repo as you can get. F-Droid even has the tarball of what it built and the build log if you want to inspect it for transparency. You don’t even need the F-Droid app to download it.
If you don’t trust F-Droid, the next best step for you is to build it yourself. Not sure why you’d trust Codeberg to host the APK but not F-Droid.