You should use MC to create the database backups (ZIP files - should already be automatically created daily) and then include those zip files in your NAS/Cloud backups. You can then exclude the MC database folder, but the Cover Art folder is not included in the MC backup so perhaps it's better to include that one. If there's a need to restore a backup, restore the ZIP file in MC, not the folder.
I don't backup the database folder. The folder I backup from my Mac to my NAS and PCloud is [User]>Music>JRiver (which I'll be referring to as "JRiver"). My cover art is stored in "JRiver" as well. I've adjusted my backups to only backup the cover art folder, my backup JRiver ZIP folder, and my media folder (the folder is called "Music"), which are all located in the "JRiver" folder. The "J River" folder (located in [User]>Music>JRiver>J River) occasionally has cover art in it as well—should I back that up too?
I restore the ZIP files in the way you described—in MC, not in the folder. I restore them using the "Restore Library..." function in MC 32.
Can you check if your PCloud or NAS backup software is doing a bi-directional sync? That may cause problems, it's best to have a one-way backup/sync (not two-way).
My NAS and PCloud backups are not bi-directional. They go from my Mac to my NAS and Cloud. I also do Time Machine backups of my Mac but those are also not bi-directional and I've updated the backup to limit it to the three folders you specified (cover art, ZIP backups, media folder).
Do the playlists disappear or do they just become empty? Are they Smartlists or regular playlists? If Smartlists, how are they defined (an example)? Smartlists can easily become blank after some tagging changes - you mention you had hundreds of them.
1.3 TB is a lot. 1.3 GB not so much.
The playlists simply disappear and it's usually about 90% of them that go missing. I have a combination of Smartlists and regular playlists but the Smartlists take up the majority of my playlists.
Here's an example of the rules for one of my Smartlists called "3-5 Stars":
([Media Type]=[Audio] [User]=[New Library]) ([Rating]=3-5 [Genre]=[],[Acappella],[Ambient],[Beatboxing],[Blues],[Celtic],[Classical],[Country],[Disco],[Electronic],[Folk],[Funk],[Hip/-Hop],[Instrumental],[Interlude],[Jazz],[Latin],[Opera],[Pop],[R&B],[Reggae],[Rock],[Score],[Sing/-Along],[Skit],[Soul],[Spoken Word],[Stage],[Trip/-Hop],[Turntablism],[World]) ~sort=[File Type],[User],[Name]