Looking for a webcam with a built in light

If you're not concerned with color temperature, bright spots, or white balance...go for it. Simple clip-on LED lights will render better results, and can typically use filters or LED adjustment to get the right color temperature. Your rig though, go with the solution that works best for you.
 
I would go with the Logitech. I tried the Razer Kiyo a couple years back and never quite liked it, at least not for the endless Zoom meetings. Maybe it’s better for recording and having it further back/off center, plus there are lighting/temperature adjustments in the app for it. It’s at least an option if you want to look at other devices.
 
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Got this. These lights aren't very bright, I assume they're for detection and color correction. Maybe this will work but maybe not.