Is there a reason a RPi or whatever with a cheap USB HDMI capture card isn't a good option? I guess there might be a minor quality loss but it should do what you want.
HDCP usually is an issue if you can't turn it off on the source. There are ways around that, though those are more than $199 if you're dealing with an HDMI 2.x source.
I thought there were cheap converters that could go HDMI 2->1?
Back in 2019 I paid $399 for a Vertex2, but if there are cheap options now in 2024, that would be awesome!
I bought a random HBVALINK branded splitter on Amazon last month for $29 that works perfectly for this purpose.
I bought a HDMI 2.0 splitter that strips HDCP a while back for $20.
Usually the lack of supporting 4:4:4 colorspace, and 4k video at anything over 30hz.