I think there are both Layer 1 adapter plugs (simply changing the wiring medium), which I would call HDMI over Ethernet,  as well as layer 3 solutions (HDMI running over IP protocol on an IP network). From what I understand, your distance is still very limited with a layer 1 solution. But you should have no delay or synch issues. Video over layer 3 (what I would call over IP) is no more limited for distance than IP over Ethernet in general of course. Obviously, video/HDMI over IP can carry at least 4K (same as over the Internet). But you might have delay or synch issues.

Also, pretty sure you can setup QoS on most switches to give the video priority on your IP network - same as VOIP (voice).

I just scanned through this - looks like it might be helpful:

http://i2.cc-inc.com/pcm/marketing/BlackBox/2019/video-transmission-over-ip.pdf