Unfortunately I got the same result that archivarix did above, nothing in CC and nothing in IA. The thumbnail had a different link than the title of the playlist so I thought I’d try that, but the wayback machine redirects to the first video on the playlist, and there’s nothing in the common crawl. I also checked the html just in case there was a track listing hidden in there, but there wasn’t.
Really appreciate you taking the time and thinking of some alternative methods!
Not sure if there is a blocker from youtube in some way, but making backups of public playlists would certainly come in handy for a lot of people.
Seeing the articles and youtube videos and other articles about how to find your YT profile URL and searching the archive - obviously it's a thing bigger than I thought, and not something I ever considered.