It’s possible that the results you see in the search are different from the ones I see, so I thought I’d point out some of the channels that I was referring to:
YT Jam Tracks
Sebastien Zunino
Elevated
Quist
They mostly aren’t known songs. They’re just extended grooves with one or two progressions each, with provided chord changes. They do have a full rhythm section, so they aren’t totally generic because they are often associated with a specific genre. There are plenty of other channels as well, if you have a more specific genre in mind.
For example, this playlist by Benjamin Harrison focuses on specific common jazz chord progressions:
Fundamentals
His other playlists are pretty great, too.
Some of these are the YouTube equivalents of the old Aebersold tapes I used many decades ago:
Jazz Standards
Learn Jazz Standards playalongs
I believe most of these actually are Aebersolds:
Charlie Goodman
Here’s a good one for practicing changes over a more modern rhythm section:
These are intended for piano players, but music is music.
It’s possible that I’m not interpreting the words ‘songs’ and ‘generic’ in the way that you mean them, though. If by ‘generic’ you mean repeated alternating chords with no genre or style, you can sign up for this free course (I have no affiliation, though I did work through the course), which includes some downloads of chord progressions. They are synth, bass, and drums, but I wouldn’t say they have any kind of a genre association or style, in any sense of the word. They are useful for harmonic workouts, though.