Thanks @YaBoiB ,
This is a Windows Server 2019 terminal server my users log in to for a virtual desktop. Apps are allowed to use the camera in Privacy settings, but Zoom is not a listed app. Only Cortana and Desktop App Web Viewer are listed. Even when looking at my Windows 10 laptop Camera Privacy Settings, Zoom is not a listed app, and Zoom works as expected on my laptop. However, I did notice that Remote Desktop was NOT allowed to use my webcam in my local machine's privacy settings. I enabled it, and now it works!
So apparently the real question I should be asking is why the other apps didn't respect my privacy settings!!
Thanks for making me look in the right place! 🙂