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.