listenonrepeat.com was up for years until last month, when it mysteriously went offline. I haven’t found any sites like it. I could just paste in a youtube link and have it play right away, and choose the start and end times for looping, and it had a count for how many times you played the song, as well viewing history (with start & end times saved) so you could easily listen to previous songs.
Infinite jukebox has more complex looping and I think is just a website, but its super cool. I haven’t used it for ages, but it may be worth checking out
I think a decent alternative would be to use yt-dlp to download the songs you listen/watch on loop most often, then use a basic video editor to cut out the start and end bits you don’t want. Plus, that means you can listen/watch to them offline using your preferred video player of choice! This, however, isn’t as good if you’re the kind of person who likes listening to new songs, and it won’t count how many times you’ve played each song.
Found somewhat recently an Android program, Musicolet, which does count how many times you played a given music file. It’s on Google Play and as an APK through the devs’ site.
I don’t know whether it has all the features you mentioned, but https://www.youtuberepeater.com/ is still up
