After exploring, and experimenting with SoundCloud's API - it's not possible to find what playlists contain a certain song...
However, SoundCloud uses a simple URL format to show which playlists contain certain songs - https://soundcloud.com/ARTIST/SONG/sets
For example: https://soundcloud.com/ultrarecords/cheerleader-felixjaehnremix/sets
Is there any way to scrape the playlist IDs off a web URL such as the above? I've tried to curl the page and it doesn't give the IDs of the playlists.
It is possible.
Go to the site, open the developer console, go to the network tab and look at the xhr requests.
While looking at the requests you will find these endpoints, they are part of the next api version:
https://api-v2.soundcloud.com/tracks/150483650
https://api-v2.soundcloud.com/tracks/150483650/playlists?limit=10