I've tested on Google Meet and Zoom, it allows me to display equations and quick sketches to collaborators and students. There are much fancier purpose-built document cameras with similar functionality, but these are mostly sold out on Amazon, due to the increase in remote work and online teaching. The particular web cam I am using (see link above) has a manual focus, in case the software auto-focus is unsatisfactory.
Both Google Meet and Zoom allow to switch from the default internal camera on my laptop to the external web cam (a simple toggle in Settings). The web cam is auto-detected on both Mac OS and Chrome -- I did not have to install any drivers.
The plastic clip I used to attach the web cam to the lamp is from the kitchen (Bed Bath and Beyond). Tape would also work as the web cam is very light.
Here is the rig in action, using Google Meet. I write on the pad and my colleague can see it very clearly.