I've personally had a great experience with the Magewell USB3 HDMI capture device, which I believe is also UVC - requires no drivers on Windows/Mac and claims to be Linux compatible. Slightly cheaper than the u-tap.
Can do lossless capture with extremely low latency, which is pretty nice - it's good enough that I've been able to play console video games on it directly instead of plugging into a TV.
https://www.amazon.com/Magewell-HDMI-USB-Capture-Dongle/dp/B...
Can do lossless capture with extremely low latency, which is pretty nice - it's good enough that I've been able to play console video games on it directly instead of plugging into a TV.