Server only runs for a few minutes

Plex Media Server NAS & Devices
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The problem is with your photos. There are ~12000 such error messages:
Nov 15, 2021 06:52:43.989 [0x7f9b15e90b38] ERROR - [Notify] Failed to add watch for "/volume1/photo/default/default Previews.lrdata/C/C9BE" (28: No space left on device)

I do not have photos on my Synology, so will be of limited help. However, here are some things to check:

  1. Are you really out of space on /volume1?

  2. Do you have Synology Photos installed? Plex seems to have issues with it. See DSM 7 - Synology Photos shared folder issues with Plex - Please read

  3. You may have exceeded the number of folders that Plex can monitor. See FAQ 16: Increase the number of folders Plex can monitor for steps to increase the default value.