Probably 48k. And it might be unusable because someone chose to write the Audio Monitor so that it locks to that device and adjusts the buffer as needed *instead of resampling*! I have no idea in what universe that's useful, but that's what they did.
Any amount of clock mismatch at all will either cause underruns or the buffer will grow to the point of being uselessly delayed. How quickly that happens depends on the amount of mismatch. For nominally the same setting but from a different physical clock, it might take a while; but for different settings, it happens pretty quick. If *Windows* resamples for you, then that can save your bacon, but OBS is still providing its internal sample rate to that external resampler.
That said, I really don't see a benefit to anything beyond 48k. Contrary to audiophool belief, it doesn't sound *any* different *at all*. Nyquist (the highest frequency that can be represented accurately) for 48kHz is 24kHz, which is already beyond human hearing. And no, we don't perceive harmonics of that upper limit.
For timing and other things, see here:
www.xiph.org
With THAT said, I *am* designing a bare-metal project (no operating system at all) to use 96kHz audio (or possibly even faster),
not for the non-existent sound quality, but to allow the analog <-> digital converter chips themselves to use less aggressive lowpass filters, which in turn provide fewer samples of latency in addition to having less time between samples. This is for a mic and speaker physically close to each other, and the entire system has to line up with the speed of sound over that short distance. Again,
it has nothing to do with the sound quality!
OBS has enough else going on, not to mention a multitasking operating system (Windows, Mac, Linux, etc.), that it needs to have a buffer that can fill up while it does everything else. Then it processes that buffer, and lets it play out at the end while it does something else again. So it's completely impossible to realize that benefit, and thus no point in running the converters that fast.
No need for anything beyond 48kHz if you're using enough of a buffer to make a multitasking system work.