You should check out Synergy (free version.) It may do what you need at no cost. It will let you have kb/m plugged into one computer, with each computer getting its own monitor plugged in side by side. They're connected via LAN. What Synergy does, is when you move your mouse over to the other screen, it will just carry on to the other screen and you can now use the other computer with the same kb/m. Latency is unnoticeable if they're using Ethernet.
https://chocolatey.org/packages/synergy
Ahh true, I didnt catch that about both monitors at the same time. I don't see any kvm that support dual monitor hdmi and displayport, but you could use a display port to hdmi adapter on the work computer to the kvm.
How integral is the GPU in the work pc? If its only to drive displays and not for any kind of serious workload, you could put a new cheap gpu in it with hdmi. Seems much more cost effective and simple than trying to find a kvm with hdmi and dp input.
Oh, it's a laptop. Alternatively, you could get a DP kvm, and run the DP to hdmi cable from your pc, and if the cable still doesn't work, maybe just an adapter.
Me either. And from what I did find, if one did exist, it would be hundreds of dollars, not worth it when you could just throw a GPU with dp in your home pc. Unless that's a laptop too.