Having stepped away for a bit and come back, one possibility might be to use a USB video capture device.
There are borescopes designed for phones, that are essentially small USB cameras with long cords. If *that* works, then maybe a video capture card will too, and you can plug that into a physical output of the OBS machine.
You'd be wired, but maybe that's okay? If you must be wireless, then you might stick a wireless HDMI extender in there, but I've never used them and so I can't vouch for their quality or the pitfalls.
Speaking of pitfalls, USB video captures themselves have plenty! Stick with the name brands, and expect to pay about $80 to $120 for a good single input.
The cheap ones are garbage, deceptively marketed, and their haphazard design and manufacturing makes them effectively random as to what works and what doesn't. The sellers profit regardless, because they're too cheap to be worth returning. Don't go there.