Thanks again for your help. Unfortunately, I keep getting the message about indirect playback (via proxy relay) when I’m not on my LAN (for example by turning off WiFi and choosing 5G on my phone). Yesterday I was trying to remove the addresses from the option “List of IP addresses and networks allowed without permission” under PMS Network. Then I could no longer “see” my server in PMS! With the help of this excellent article I was able to solve the problem. By the way, the addresses have disappeared and PMS is working fine again. I had already encountered this problem before (for which there is no solution yet).
Anyway, I think I have to find the solution to the problem with Tailscale in the option “LAN Networks” (by specifying the IP range of my Tailscalenet here) and/or “URLs for custom server access” (by entering :32400) on my PMS. Because if I play via PlexAmp without Exit Node on in Tailscale(!), then I see the (local) IP address of my phone. If I turn on Exit Node, then it plays again indirectly (and the Dashboard in PMS reacts very slowly).
If you - or someone else on this forum - can confirm that, I will get started on it. You will understand that I have become a bit more careful with trial & error on my PMS ;-).