Thanks for sharing this, I'm the author of Generative.fm and the music systems on it.
Just wanted to pop in to tell OP that there's a recording feature built in to the site, and everyone is free to use the recordings for whatever they'd like - I just ask that you give attribution (it's licensed under CC-BY 4.0). Though, there's no configuration and I don't use AI, if that matters.
EDIT: I forgot to mention it's free, and all the music is ambient.
It is due to certain settings in the browser profile that I use for everyday surfing. Without giving too much information, let's just say that although some things are blocked, popular music and video streaming web-sites still work, so I guess this one should also work. It works in a clean profile with default settings in the same browser.
https://generative.fm/