Maybe a jitsi meet room with webcam would do. When doing it with a computer instead of a phone, you can set up OBS virtual camera (1 click thing) to add a filter that makes it grayscale, but that's slightly more clicks.

Regarding the warning for the fdroid app that was recommended by an other user, it might be ok if you place a clock with second-display in the view, so that you know if it has frozen.