adapter. I can connect the DVI monitor directly to the desktop or laptop with a DVI to DP adapter or a DVI to USB-C adapter and that works. But if I plug anything through a new KVM switch that I bought, I don't get an image on my screen for either computer.

Do I need to suck it up and buy a monitor that is native DP? I assume so, but it seems dumb that direct will work for both computers but through the KVM I bought, neither will work.