PMS Settings → General → Show Advanced
Based on error messages, it looks like you’ve database corruption.
Jan 15, 2020 17:46:21.015 [0x7f38e1656740] ERROR - SQLITE3:(nil), 11, database corruption at line 64757 of [bf8c1b2b7a]
Jan 15, 2020 17:46:21.015 [0x7f38e1656740] ERROR - SQLITE3:(nil), 11, database corruption at line 64798 of [bf8c1b2b7a]
Jan 15, 2020 17:46:21.015 [0x7f38e1656740] ERROR - SQLITE3:(nil), 11, statement aborts at 25: [insert into plugins (identifier,framework_version,access_count,installed_at,accessed_at,modified_at) values (:plugins_identifier,:plugins_framework_version,:plugins_access_count,:plugi
Jan 15, 2020 17:46:21.016 [0x7f38e1656740] ERROR - Exception inside transaction (inside=1) (…/Plugins/PluginDatabaseState.cpp:135): sqlite3_statement_backend::loadOne: database disk image is malformed
Jan 15, 2020 17:46:21.016 [0x7f38e1656740] ERROR - Exception inside transaction (inside=1) (…/Plugins/PluginDatabaseState.cpp:49): sqlite3_statement_backend::loadOne: database disk image is malformed
Jan 15, 2020 17:46:21.016 [0x7f38e1656740] ERROR - Error: Unable to set up server: sqlite3_statement_backend::loadOne: database disk image is malformed (N4soci10soci_errorE)
Repair a Corrupt Database has information on how to attempt repairs.
If you do not need to keep metadata, users, watched status, etc, it may be easier to completely remove Plex from your NAS, then re-download the package from plex.tv, and start over.
See this post for info on completely removing Plex from your Synology. Your media will not be touched (unless you have it in the Plex shared folder, which is a bad thing and will cause problems).