An old phone is probably your best bet - you do not necessarily need that big of a sensor to get decent video. As long as you can provide enough light to keep the noise down and the lens (there are addon lenses for phones that are not half bad) is decent you can achieve probably what you want. The phone will have the necessary horsepower to actually process the video - I think that is probably the main issue vs a webcam

More importantly though why does most conferencing software limit us to such low resolutions? From what I remember Zoom is still max or 720P which is pretty damn terrible....