I've been using a "cheap" Logitec USB A headset for the last few month with my Pro X and it's never given me a problem. I've used it with the Surface Dock (on loan from my employer) as well as via a USB A to USB C adapter. I've read of Bluetooth issues, but find it odd that you're also having trouble with a wired headset. I don't have any USB C devices (esp. not headsets) to try, but there must be something about the specifc device you're trying as I don't think the issue in inherent to the Pro X or I would think I'd be having issues too.
I've used mine with Google Meet, Zoom, Amazon, and Teams that I can think of.