For no delay between both streams, I don't think there is a way around a third computer with a capture device for two video signals:
Computer A's HDMI output ---> capture device input 1 --> capture device output 1 ---> monitor A
Computer B's HDMI output ---> capture device input 2 --> capture device output 2 ---> monitor B
Another way would be to multiplex the signal and feed one signal into a monitor and capture device port each.
You can then use OBS to composite both streams, which should be as sync as possible.
Other solutions involving network communication will definitely result in both streams not being sync, to a certain degree. If you want to do a coding session or something else desktop-focused (i.e. not gaming / video), then TeamViewer (or similar) is a pretty good option. Use window capture, it will be captured even if other windows are on top of it. But if you minimize the window, it will go black. The delay is pretty low thanks to the codec used, but isn't really suited for fast changing visual content.
