Only tangentially related but if you already have a popular Logitech webcam (like the C920) chances are you can find a kit to mount C/CS/D-mount lenses on it, like with this one: https://www.kurokesu.com/shop/C920_REWORK_KIT2
C/CS/D mounts are for CCTV camera so you can find new and used lens for cheap. They will not fix a cheap/bad sensor, but they will definitely get you extra flexibility in what kind of framing/shot you can do.
This right here is the best solution I've found. I have their Brio kit w/2.8-12mm CS lens and it's excellent in a small package. Low light conditions are still a challenge due to the tiny sensor.
As a bonus, you can disconnect the built in mics and opt for a nice boom mic with a hardware cut off switch.
C/CS/D mounts are for CCTV camera so you can find new and used lens for cheap. They will not fix a cheap/bad sensor, but they will definitely get you extra flexibility in what kind of framing/shot you can do.
As a bonus, you can disconnect the built in mics and opt for a nice boom mic with a hardware cut off switch.