DSM 7.2.2 upgrade & plex fresh install - 'claim server' won't work

The claiming problem, as you describe it, is usually network problems. The NAS cannot communicate with hosts at plex.tv.

Check network basics - IP address and mask and default gateway. Use a public DNS server - 1.1.1.1, 8.8.8.8, 9.9.9.9.

Also, sync the NAS with a public NTP server. If the NAS time is wrong, claiming will not work.

Question: Do you still have the /plex shared folder from DSM 6, with database files in the /Plug-in Support/Databases directory?

If yes, you can recover your old Plex server. See Struggling with migration from DSM 6 to DSM7 - #2 by FordGuy61.