How can I transfer playlists from an old music library on my iPhone to a new Mac mini hard drive?

Due to processing slowness, I had to replace my hard drive with an SSD. After doing so, I created a new music library in Apple Music by importing all of my media from its existing location, an external hard drive. However, in doing so, I was not able to recover the playlists from my old music library.

These playlists do exist on my iPhone and I'd like to export them from the phone to the Apple Music library, but it seems that in order to do so, I must first agree to sync music between the Mac and the iPhone, which I'm told will delete everything from the phone. Doing this would delete the playlist info I'm trying to transfer, though. I've looked for a way to export the playlist to XML on the phone, but it doesn't seem to exist.

Is there any way to export the playlists, start to sync music again with Apple Music, then restore the playlists to both Mac and phone?