Say you want to always use your desktop as the main device. You would plug everything onto the desktop, and have the laptop only plugged into the monitor (this is easier if you have two monitors so you can make one of them be forever desktop and the other forever laptop, so you don’t have to keep switching the monitor inputs).
You will install Barrier on both of them, then configure your desktop to be the server and the laptop to connect to it. So for example suppose you keep your laptop to the right of the main screen, if you configure this properly you will be able to move your mouse from your monitor (desktop) to the laptop screen and click and write there even though the mouse and keyboard are plugged onto the desktop.
From there it’s a quick jump to having both plugged onto the same monitor and switching the input and moving the mouse right until it shows up.
Now this is not perfect, but it lets you use both PCs without a KVM. But just so you know I used this for a couple of years and bought a KVM and have never looked back, so since you’re already using a KVM this might feel janky or slow, but give it a try.