I’m not an android dev nor am I affiliated with the f droid project so this might be wrong: As far as I know f droid started using an Android built in mechanism for updating. It has to request permissions to install and update apps at all and then it has to ask once for each individual app.

So you allow it to update apps and install X. Then once X gets an update you will be asked whether f droid is allowed to install ist. When the next update for X comes f droid will be silently allowed to install it.

As far as I understand it’s just how this kind of permission works on android.