I’m not an expert on the process, but anyone making a custom repo should be able to store the F-Droid repo on GitHub.

It looks like you wouldn’t need to make the app open-source either, as it should be capable of just accepting an apk file. (and possibly auto update from any GitHub releases page, not sure on that though)

Again, not an expert, I haven’t made an F-Droid repo yet myself, so I may have understood something wrong, but it looks relatively straightforward according to their guide

This wouldn’t make it available to users through the default preinstalled repo in F-Droid (which is heavily privacy-focused and limited in scale) but it would allow any user to just click a link or scan a QR code to add your repo to their F-Droid app.