I just recently purchased a new 16' MacBook Pro and was having the exact same issue (with exact same results from troubleshooting) as Orestes on the original post. I finally got 95% of my desired end result by doing the following:
Consolidation
In iTunes on my original machine (MacBook Air), I consolidated files being sourced from outside my iTunes folder (if any) by clicking File > Library > Organize Library... > Consolidate Files > OK
File Transfer from Old MacBook Air (iTunes) to New MacBook Pro (Apple Music)
I copied my entire iTunes folder from the original machine to a flash drive (iTunes folder was located in Users > MyName > Music > Media > iTunes) which took about 20 minutes to copy for ~32gb worth of music.
I inserted the flash drive into the new machine and copy/pasted the entire iTunes folder into my new Media folder (Users > MyName > Music > Music > Media).
Automatically Add to Music Folder
The iTunes data I brought over contained a folder called "Automatically Add to Music" - I took all the other content in the folder and put it into this folder so my new file path is: /Macintosh HD/Users/MyName/Music/Music/Media/Automatically Add to Music - this was per a suggestion earlier in this thread. I made sure it was linked to this path by clicking Music > Preferences > Files > Change... and selected the "Automatically Add to Music" folder from the finder window.
Doing this brought over all my songs (with some duplicates, but nothing major) into the Apple Music search/song/artists libraries. However, my playlists were still not showing.
Import Playlist
Per Orestes' suggestion, I took the File > Library > Import Playlist approach and selected the iTunes Music Library.xml file as well within my iTunes folder on my FLASH DRIVE - this is important because for some reason after I added these files from the transfer above into the "Automatically Add to Music" folder, the xml file as well as the iTunes Library.itl file disappeared; I was able to just use the xml from my flash drive and it worked fine. That said, I believe this xml file was created after the consolidation (?) - please correct me if that is not the case. Regardless, I now had that file and was able to click it to import the playlist.
All of a sudden all my playlists came over with about 98% accuracy - for some reason 2-5 songs from each playlist were missing but I went through one by one and added them, as they had made it through the migration. All my metadata though was now showing "01/20/20" (today) as the date added. The music which was bought from the iTunes Store would show all the correct metadata regarding original song release date, etc. but the information from my MacBook Air would essentially be overwritten by this migration.
Hopefully this was helpful - I didn't exactly document as I was going since I was working on this for about 4 hours today trying various tactics, but what I did above worked for me! Good luck folks; hopefully they properly patch this at some point.