[echohack5]

Maybe the closest thing to this is a Blackmagic box of some sort. I use a the Ultrastudio 4K to capture 4K60 output, pipe through OBS and pass through as well.

Will run you $1K though. Corsair/Elgato has some solutions in your price range but the devil is in the details of precisely what you're trying to accomplish.

[evilduck]

An HDMI splitter (i.e. an HDCP down converter/stripper) and a video capture dongle or card can be had for like $60, plus a computing running OBS. It’s not an elegant small box, but it’ll get the job done for lower resolution needs.