You could install OctoPi and use that camera feed. It’s a little overkill compared to motioneyeOS since it’s originally meant for monitoring and controlling 3D printers, but I’ve had better luck getting OctoPi to set up a camera feed than motioneyeOS, which was abandoned by the developer years ago.
You could install it on the NUC, plug in a camera, and it should just work. Then use whatever remote access method you want, i.e. tailscale, port forwarding, VPN, etc.
She has her own show too, The Mindy Project, and it’s further evidence that she just plays herself in everything.