Can I recover lost playlists from Time Machine backup on iMac running Sequoia?

My old 2017 Imac was in a reboot cycle demise, so i took it to the genius bar for repair. The unplugging seemed to fix the problem temprarily, but all the music files and playlists were lost from Music app.

The problem continued so I bought my new (refurb) Imac, with its sequoia upgrade. Finally found the music files and imported them, but the playlists (a lifetime's work) seem to be lost.

Can I get them back from a Time machine backukp of the old machine?

[Re-Titled by Moderator]