As you can see in the above message, PMS stores all meta data by default in /var/lib/plexmediaserver/Library/Application Support/Plex Media Server: media infos, thumbnails, chapter images, …, and the intermediate data created by the transcoder. Your 8 GB for this storage is awfully small (the storage for / relevant here) . In fact, too small.
At least, change the “Transcoder temporary directory” in the PMS Transcoder settings and make sure this directory is writable by Linux user plex.
You should probably also consider to move the complete PMS meta data storage:
