Just want to update everyone on this, I have fixed the issue.

IMPORTANT NOTE: Make sure you have a backup otherwise this fix won't work.

Firstly, this weird error I was getting wasn't helped by the fact "iTunes" became "Music app". The folder structures are similar but when macOS updated to Catalina it didn't do good job of the folder structure.

iTunes folder structure was - iTunes>iTunes Media>Music
Music app folder structure was using both the above folders and a new one - Music>Media

Also the important file that memorises your library and playlists etc. for iTunes was the "iTunes Music Library.xml"

For Music this is no longer the case, this file is now called "Music Library.musiclibrary" This file is updated continuously due to Apple Music.

You can export your library as .xml file but then on "Music Library.musiclibrary" is used.

I thought simply adding the files back to the folder and opening iTunes using option key and selecting the file would work, but when syncing with Apple Music it gave errors for my entire library, it also duplicated playlists and music and caused havoc.

To solve this and start fresh you need to reset you cloud library. Firstly keep a copy of your music backed up and move to separate location. Then remove the files in the current folder "Music app" Then delete all music in library by going to songs and delete. Don't worry none of your files will be deleted as you have backed this up and moved to external hard drive etc!

Once this is done check your other iOS devices and clear any music stored locally and unsync. Music app should now be empty to double check this signing out of Music app and quit Music app. After a few seconds open Music and sign back in. Check under preferences that sync is on. You can turn this off and then sign out to ensure that your cloud library is empty.

You can also check by opening Music by holding down option key and create new library call it "Music 1". Ensure you are signed in and sync is checked. Wait a few moments to see if anything loads. Your library should be empty including playlists. If anything appears, repeat the above until Music app is in a blank state.

Now before you load your files back in go to preferences and untick sync library to cloud. This will make Music app become an offline version. Quit Music app.

Now create a "copy" (don't move your files jut yet) of you music library and move to your desired location. Now open Music app by holding option key and selecting the "Music Library.musiclibrary". This should load your music library as you last left it, you can check this by the date. This file is always updated so the minute you open Music app the date will change to todays date. (Thats why keep a copy).

If you library looks as if it was how you left it, first export the library into .xml file. and save (just in case measure, will explain below).

If you have two folder structures one from iTunes and one from Music app before you sync to cloud, "consolidate" your library! This will "copy" your music from iTunes folder to "Music app folder" Check that all music has copied, it will tell you how many songs have been moved. Also "command key and forward slash" bring status bar up (bottom of screen) and tells you how many songs and GB you have.

Any missing files you can relocate (using finder) and Music should find them, if this was the case re-consolidate library again until all music is in one location. "Music>Media"

Now you have all you music in one place, its best to create another backup of the clean data, call this version 2, or whatever you like. You can also export the library.xml again. Now you have your original files and nice fresh second copy. Move this to separate location!

If you prefer to fix your library and playlists before syncing (recommended) you can do so now and create a backup, so you don't have to repeat these steps again. Remember backup and to export your library.xml file otherwise you have to re-configure all your preferences again. It will save you the time already put in tweaking Music as you like to view it.

Once you're happy with everything, quit the app and wait a few moments. Then re-open Music app. Go to preferences and tick "sync". Because we emptied your cloud library it should now start to update and either match and upload your music. You can check this by the cloud symbol. If you go to"view as songs" this will bring up the classic list view (which I prefer) and then right click on a column and select "cloud status. Remember to stay in on songs under library to see all your music. 

The cloud symbol should be dotted and once matched or uploaded will disappear. "Cloud status" should also say matched or uploaded. Any errors you can check which will say either duplicate or error. This should be either zero or very little. (I experienced less than 10) Any failed attempts you can right click the song and selected "add to library" and it should match or upload.

This worked for me, the only thing that took time was to clean up my playlist "view as songs" (list view), Music app doesn't have default option to select all playlists and "list view". I have kept my original backup and this new copy just in case. If you use time machine I suggest to start using it.

It always important to backup YOUR data.

As mentioned earlier the "Music Library.musiclibrary" is updated continuously and memorises your library, playlists, formatting etc. under the Music app. I don't like importing much as, when you import your library it imports using the current date and can ruin any smart playlists such as "recently added".

If you were unfortunate to lose you formatting because of the "Music Library.musiclibrary" being corrupt, you can re-import this using the .XML file the one you saved out earlier. File>Import. 

This will bring back all your playlists and formatting however any smart playlists such as "recently added" won't be the same as it imports your entire library as of todays date. Which I think is second best to recovering your library but you can start from scratch with "recently added" playlist.

Remember your actual music from ripped CDs is important data and also "Music Library.musiclibrary". Any music you obtain from Apple music you can obviously retrieve again.