Maybe FreshRSS with some extensions?
I saw a recent commit to fire an event when saving a favorite, so probably you can get an extension to send the link to something like archivebox for the pages you favorite.
I’ve just fiddled with an already created extension, but they seem fairly simple to create your own easily.
Of course you can inject JS so you could make it more complex if you want.
The video in YT and the music played in YTMusic are two different uploads, you can easily get one in YT by checking the YTM URL and getting the ID. So yeah, yt-dlp should get you only the song if you created a playlist with only songs instead of music videos.