I have a cheap $15 USB web cam hooked to my Pi 3b and Octoprint and it works fine. I think I used a webcam on a latop/PC once and that was for a doctors appointment and on my Macbook.
Is the webcam just to watch the progress of the etching like when 3D printing? If so couldn’t you put Octopring on the Pi with the webcam and watch that way? My printer with Octoprint is running so I can’t check and see of the camera still works with the printer off but I think it does.
Lowteck, I agree with Gramps: why not use a low end Pi, like a Pi Zero 2 W? You can put OctoPrint on it and run the camera completely independently of the etcher. If you have a PiCam, that will work too.
I have my 3D printer in another room, but it is in a place where I can sit comfortably and watch TV and glance at the print to see if things are running ok. The laser etcher is located elsewhere and the chair is a hard wood chair and the laptop has to be attached to the etcher and because of a fire problem, it has to be continuously watched with not way yo watch TV. I have a Lightburn approved camera ready to hook up, but there again the laptop has to be attached. This is why I am trying to attach the Pi or Pi’s. You have to test to learn.