How to use the green screen just locally
Since OBS is using a very old browser inside, the green screen effect inside VDO.Ninja wouldn't really run well within OBS itself, and even if it did, accessing the camera from a browser-source is a hassle to setup.
What you could do though is use the Electron Capture app, and then just window capture the local preview output. You can hide the interface UI and access any camera/microphone changes via the Electron Capture's right-click context menu of options instead.
Electron download link: https://github.com/steveseguin/electroncapture/releases Getting this working is not complex; pretty easy once you do it once actually. Sample URL to enter into VDO.Ninja: