Are you running Plex Media Server on the DS214 or on a PC?
The log files are from a Windows 10 system.
Dec 03, 2021 23:18:41.755 [7820] INFO - Plex Media Server v1.24.2.4973-2b1b51db9 - Microsoft PC x64 - build: windows-x86 windows - GMT 01:00
Dec 03, 2021 23:18:41.755 [7820] INFO - Windows version: 10.0 (Build 19043), language de-DE
Dec 03, 2021 23:18:41.756 [7820] INFO - 4 2712 MHz processor(s): Architecture=0, Level=6, Revision=36361 Processor Identifier=Intel64 Family 6 Model 142 Stepping 9, GenuineIntel
Dec 03, 2021 23:18:41.756 [7820] INFO - Compiler is - MSVC 1924
Dec 03, 2021 23:18:41.756 [7820] DEBUG - "C:\Program Files (x86)\Plex\Plex Media Server\Plex Media Server.exe"
Something went wrong with installing Plex Media Server on the DS214. There should not be a recycle folder in the Plex shared data folder. Also, the username should be plex, not PLEX.
As the Plex Media Server folder is empty, there is no metadata, play history, etc to save.
I suggest completely removing Plex Media Server from the DS214 and starting over from scratch.
Step 4: Manually install Plex Media Server on the DS214
Following the steps in the Installation & Setup Guide linked above, perform a manual installation of Plex Media Server with the file you just downloaded from Plex. Do not install the version provided by Synology, as it is approximately two years out of date.
Removing the app, the plex user, and the plex shared folder will take care of permissions, etc.
The user and shared folder will be re-created when you re-install Plex on the DS214.
After re-installing Plex on the NAS, you will have to give the user Plex at least read-only permissions to where your media is stored. This is covered in the Install Guide immediately after the “Installing Plex” section.
Note that the Plex shared folder is reserved for use by the Plex Media Server application. Do not place any of your movies, shows, or other media in that folder or any subfolder. If you do place media there, Plex will not run correctly. There are warning messages, but some videos on YouTube give incorrect advice.
When you install the current version, it will create a shared folder, /plexmediaserver, and move the Plex data folder (the old /Plex folder) to that location. See the “Packaging 2.0” document for details. Depending on the amount of data, it might take some time to perform the migration (minutes to hours). Don’t stop it, just let it run.