Both systems were running Debian 11 and plexmediaserver 1.30.0.6486-629d58034.
I changed the Port forwarding on my router from the old internal ip to the new one and checked that i can reach the plex server from the outside (using my external IP and port 32400).
The Settings page of plex, when accessed over the internal network IP or the external IP (also tested from a different internet connection) shows that remote access should work: