@zyax39 The membership for these streaming sites are access fees only. You are not purchasing songs per se'. With Tidal for instance, and perhaps the others, I am not sure, but a "tag" of the music you wish to stream and keep in a library or playlists, are reference markers only. If you take your streamer off line, your referenced music will not play.
The only was of 'keeping" the music is to record it, most likely via microphone in front of speakers.
The streamers have us locked up and tight.