Mac sometimes goes zombie using a KVM switch

I use a KVM switch (an ezcoo) on my desktop, to switch between a Mac mini, a Linux box, and a Windows box.

Sometimes when I switch away from the mac, and later come back to it, the mac is in a bad state. The screen goes to sleep because it receives no signal. If I press lots of keys and move the mouse, the mac beeps loudly, so it’s definitely not asleep, and is receiving keyboard-mouse input.
I used to resort to shutting down the mac via the power button when this happened.

I’ve discovered a better way: putting the mac to sleep before switching away from it with the KVM. The zombie behavior disappears. The mac wakes up properly when you come back to it, every time.

There’s a bit of a challenge here in knowing if your mac really is asleep before you switch away. In many mac models, the power light stays solid even if the computer is sleeping¹. Tssk, Apple, shame on you. Both my Linux box (a System76 meerkat) and my Windows box (a Lenovo mini PC) have a pulsating light to show they’re asleep. Take note, Apple².

In my case, I have a USB microphone connected to the KVM switch. When the mac is properly asleep, the light on the mic turns off.
Sleeping the mac before switching away works beautifully every time.