Managing my playlists on my Ipod Nano 4th generation on my new mac

For years, I have used my Ipod for an exercise class. I connect it to my mac in itunes and I would change the order of my songs for my next class. I have about 20+ different playlists that I was able to rearrange the songs in any order. I bought a new mac pro and everything was transferred to from my old mac to my new ones.

We then found that when we opened the new mac, there was no more itunes...only Apple music. We connected my ipod with an adapter for the new mac and we could find all of my songs but no playlists.

I cannot believe that my playlists are now unavailable for me to work with on my computer. There must be a way. IF I HAD known they would've been lost, I would have asked sooner how to save the old itunes on my old mac. I would so appreciate it someone could please figure out how to help me make my playlists on my ipod workable again. Thanks!