Not sure, but had you seen Jabbers VR streaming/recording tips here (I put the timestamp to 12:06 if it doesn’t work)?
I’ve actually used OBS in VR but for another typical bizarre and frogish use. Sigh, almost embarrassed to say this as it’s off-topic and it’s so incredibly hacky, but whatever… 
Goal: I wanted to use X-Plane X-Life in VR.
Steps:
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Set up OBS to sample a screen portion rectangle of where the ATC comms window appears on X-Life in the X-Plane 11 VR view mirror.
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Resize the OBS window to just show what it would record, i.e. make it a long rectangle, turn off the other OBS panels inside the app. I used two monitors, with X-Plane on the left one and OBS on the right.
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Use Oculus Core 2, i.e. once in VR press the ‘Oculus button’ to see your home. Choose ‘desktop view’ (in my case Monitor 2, that is showing OBS) and view Monitor 2.
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Grab the shown OBS window from Monitor 2 desktop and move/resize it, so in VR it’s in your view and readable, but on your right hip, i.e. not in the way of your main view out the front of the cockpit. Make sure you ‘pin’ the window, so that when you press the ‘Oculus Home’ button again the pinned window stays up in your VR view.
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Map up keyboard shortcuts for the tab selection and transmit choices in X-Life. It has keyboard shortcuts already, so you can set a HOTAS hat to press ‘Alt+1’ when pushed forward etc.
So that allows me use X-Life in VR, using OBS not to record anything but just to sample a bit of the screen and provide a dockable window so that Oculus Home can composite in my VR space.
I did say it was frogish, right? 