I have the very same problem.
A clue: when I install OBS via the distribution links, droidcam is recognized within OBS.
When I install OBS via the 'software installer', droidcam is NOT recognized within OBS.
The two types of installations seem to be able to co-exist, with the one recognizing droidcam, and the other not. For other reasons, I wanted to have only one OBS installation, and thus must still solve the fundamental problem.
I've yet to figure out the difference, but the solution is within these clues.
I am running Zorin OS, which is an Ubuntu distribution.