Getting my playlists that were originally on my phone back on my phone

I recently plugged my iPhone SE 3rd generation into my MacBook Air (2020) in order to transfer some photos from my phone onto my computer. When I did this most but not all of my playlists disappeared from my phone. They are all perfectly in tact exactly how I had them on my desktop but when I try to sync them back onto my phone through the finder every single song that I ever added through Apple Music does not appear on my phone. Only old MP3 purchases and stuff I added via CD from old libraries I've transferred over the years. All I want is for every single song on the playlists on my desktop to transfer to my phone exactly as is. It seemed to have no issue going the other way even though I did not intend it. I feel like this should be very simple and I must be missing something.