App not syncing new albums added in Jellyfin

Yes your server bugs:

2024-06-19 13:19:14.912 Verbose/JellyfinLogger: <-- [784] Error processing request.
2024-06-19 13:19:14.912 Error/JellyfinLogger: Request Error: 500 [Error processing request.]

The complete Jellyfin side error will probably tell you more.

But this is probably Jellyfin provider not syncing - #4 by Tolriq and you need to fix your docker configuration.