The current OBS plugin depends on background removal functionality which was removed, pun intended, from the 2.0 version of the RealSense SDK. The newer D4xx cameras only work with the new SDK.
However, the new SDK does include some *example code* for background removal, so I got it working by modifying the align-advanced code sample to transmit NDI using the NDI SDK (because I use NDI extensively anyway in my streaming). I also set it to use a pixel format with alpha (BGRA) and had it fill in the background pixels with transparency instead of the color grey. OBS magically does the right thing with this.
It is equally plausible that this approach could be wrapped up in a new OBS plugin.
If that sounds like more coding than you want to take on, my other suggestion is to launch "rs-align-advanced.exe" which is in the "tools" directory of the RealSense SDK 2.0 installation, then do a window capture of that, and apply a chroma key filter on the grey background. I have not tested that but it may work.