with the GE300 I only use send/return loop, but no MIDI. The mentioned presets also do not work when I just use the H9 as a standalone pedal. Which is strange because it used to work without any problems a few days ago. And now I'm just wondering how I could fix it.

Have you tried reinstalling the latest firmware using the Direct Updater? You should also do a full factory reset after that (powering up with black encoder and right footswitch pressed and held)