Handmade HDMI capture card for Raspberry Pi and software
reddit.com
reddit.com
Mouser: https://www.mouser.com/ProductDetail/Auvidea/70501?qs=EU6FO9...
Datasheet: https://www.mouser.com/datasheet/2/864/B10x_technical_refere...
Edit: Theres also this one on Amazon: https://www.amazon.com/gp/product/B0899L6ZXZ/
I looked at the auvidea link that kayfox suggested, and could probably implement it in software on an RPi. But that has limited resolution and frame rate (25 fps).
For a feature built into most projectors, I'm surprised there's no products to do this.