Synergy works with multi-monitor (for me at least). I've been using it for close to two decades. Outside of the Linux kernel, it is probably the single piece of software I've used the longest.

I use barrier across 4 monitors and three devices, works fine.

Nowadays you have to look at the logs and search through a pile of github issues to find the right solution to make it work, but once it's up it's pretty trouble free.

Only real pain point is clipboard sharing, which works for small clipboards, but, copy too much text and it takes forever to switch.