When encountering issues with claiming Plex server, there are a lot of Reddit posts about this and possible solutions to the problem. There are even utilities you can download that allow you to force the claiming of the server, such as ClaimIt.
After a full day of trying to make sure my plex is working and not getting anywhere, as I was getting errors for a secure connection, no rights to my own media, and on and on, the issues seemed to be all over the place. Here is how I fixed my setup, which might be helpful for you.
I am running Synology DSM, with a Docker image of Pi-Hole for DNS and a Plex server running on the same hardware. Everything was fine until one day my plex started acting up and stopped displaying my library. After some messing with it and then disconnecting the server from my account, I went to reclaim it and encountered issues.
Nothing I could find online was useful for my specific scenario. After numerous attempts at fixing the issue, it was twofold and quite simple. First, since I used Pi Hole on my DSM as my DNS server, I had to log in to my router and make sure the DNS server IP was correct (mine was off by a single digit, due to migrating hardware a few days before).
The second issue that contributed to this problem was the fact that Synology’s firewall had a DNS set automatically to point to a router. As soon as both of those issues were resolved, I was easily able to claim the server and gain remote access to my library.
As this solution is nothing glamorous or special, sometimes in our pursuit of the fix we can overlook the simplest things.