I solved the problem on my own.
The problem was that for some reason I had two localhost Network Probes, not one, so a separate Network Probe could not be connected, since I had a licence for 2 pieces.
This section of the documentation helped me:
https://kb.energylogserver.com/en/latest/07-Network_Probe/07-Network_Probe.html#troubleshooting
In case anyone else encounters the same problem, here's how I solved it:
I first removed the individual Network Probe from the list, then saw that another localhost appeared, removed these two localhosts, restarted the license-service and everything worked.