New media not being added to libraries & Libraries not able to be deleted

Database corruption.

From Plex Media Server.log:

Apr 02, 2021 17:13:06.439 [0x14b553dfe700] ERROR - SQLITE3:(nil), 11, database corruption at line 79051 of [bf8c1b2b7a]
Apr 02, 2021 17:13:06.439 [0x14b553dfe700] ERROR - SQLITE3:(nil), 11, statement aborts at 11: [SELECT idx, start_block, leaves_end_block, end_block, root FROM 'main'.'fts4_metadata_titles_icu_segdir' WHERE level = ? ORDER BY idx ASC] database disk image is malformed
Apr 02, 2021 17:13:06.439 [0x14b553dfe700] ERROR - SQLITE3:(nil), 11, statement aborts at 173: [update metadata_items set updated_at=null,guid=?,hash=? where id=?] database disk image is malformed
Apr 02, 2021 17:13:06.439 [0x14b553dfe700] ERROR - Exception inside transaction (inside=1) (../Library/MetadataItem.cpp:3801): sqlite3_statement_backend::loadOne: database disk image is malformed

You have three choices: repair, restore from backup, or delete & start over. If you choose the latter you will have to re-create your libraries, shares with users, etc. Your movies/tv shows/etc are not affected.

Here’s some relevant support articles:
Repair a Corrupt Database
Restore a Database Backed Up via ‘Scheduled Tasks’

Here’s a thread from the server-docker section regarding fixing database corruption:
Problem With Corrupt databases