Just got it working. When I tried it again with Manjaro Plasma, I noticed that CUPS uses the protocol dnssd for the printer. I googled this protocol and stumbled upon Avahi. This service is started on Plasma, but not on Gnome.
When I start the service on Gnome, the network printer is found. In Gnome Settings the driverless driver is automatically selected and in CUPS I have the choice between driverless, driverless+fax and IPP Everywhere.
And with this, I can finally print! 
What I then tested again in addition: I stopped Avahi, removed the printer from the settings and then connected it again via USB and then tried to add the printer again. The model list does not show me the three drivers from before. They are only available if Avahi is started and I want to add the printer as network printer. (if Avahi is started and I select USB, the drivers are not shown.)
So I have new questions:
- Shouldn’t Avahi be in autostart on Gnome, so that network printers can be found? I just tested a fresh Manjaro Gnome in a VM and saw that Avahi is not started there either
- What has Avahi to do with the selection of drivers? Why are the compatible drivers only available when Avahi is started and I add the printer as network printer (not USB)?