This timecode format is a timestamp with seconds resolution plus a frame count within each second. To properly sync, all the timecode generators must use the same framerate. In other words, the audio recorder’s timecode framerate needs to match the camera.
The funny thing with timecode, which is hh:mm:ss:ff, is that the frame count is done at 24 frames, even at 23.976. So 1 frame of 23.976 is longer in actual "real time" duration than 1 frame at 24 fps. This can get confusing when going from and to 24/23.976.
There are more sophisticated workflows where the audio is recorded at 48.048 kHz (0.1% faster sample rate) called audio pull-up (or pull-down). The technique is used when shooting, for example, a TV spot, with a film camera at 24 fps. Since the 24 fps picture will be played back at 23.976 at the edit, the audio will follow the same speed down because it will itself play at 48.000 kHz instead of 48.048 kHz. I'm not sure that many productions still shoots TV spots in film, though, contrary to fiction where film is still being used sometimes.
But all the major VOD services, be it Disney+, Netflix, Hulu,... still mainly use 23.976 or 29.97 fps for their video distributions.
I don't know what your production company mainly works on, but these NTSC frame rates ares still the norm across the whole cinematic industry, and it's not going anywhere. It's not limited to documentaries at all.
The YouTubers etc. do use 30/60 fps more often OTOH.
So some of them might reconvert to 23.976 even when we submit 24 fps masters as per the contractual agreement. Maybe you are right. I will check.
Low budget web series shot at 23.976 even get delivered and played back at 29.97i on some local platforms here in Canada (Crave, Noovo, tout.tv), so anything's possible nowadays.
On the other end, Blurays can be encoded at both 23 and 24, and Vimeo, Youtube, etc all support 24fps. So 24 fps exists, not just on DCPs.
By the way, the loss of quality from going to/from 23.976 and 24 is not much. I've never heard any artifacts from that kind of conversion. But since cinema theatres are most likely to have a better sound system that a home system, I think it makes more sense to have the unconverted mix playing in the cinema and not vice versa.