How to get full Music Library with detail (rating, album artwork, grouping, etc) from Time Machine and Import to new Mac?

Background:

I had my old Mac (MacBook Pro 2016 Touch Bar) sync with time machine. And now, this Mac was erased and given to other people. But we before the Mac was erased, I backed up into Time Machine and also I synced Music Library using Apple Music Library on iCloud (by subscribing Apple Music). Then, the library are fully sync to my new Mac (MacBook Pro 2021 14inch).

The library is now on my new Mac but the issue is that I have to continue pay Apple Music subscription, which I plan to cancel this subscription. Therefore, once subscription cancelled, the synced library will be deleted.

Therefore, I have to get my Music Library back from the Time Machine (that previously backed up my old Mac)

System / Files Info.

My Music Library, in Time Machine Hdd, was the library since iTunes and updated to be library in Apple Music App.

My questions are:

1. What are steps needed to be done? For example, to get the Music Library from Time Machine, what need to be dene prior to importing previous Music Library to prevent duplication of files on my Music App, which is currently sync using Apple Music Library via iCloud.
2. How to import my library from Time Machine to the new Mac. The library to be imported should include all info. that I had organized earlier e.g. Album, Rating, Grouping, Album artworks, etc.
3. What else to recommend?

Thank you for help.