> some modern AMD graphics cards have USB-C

This should be VirtualLink, which was an attempt at a standard connector for VR headsets. It's basically limited to RTX 2000 and AMD RX 6000 series GPUs. Since it's for VR, most implementations should do data, and it does add 12V for power. The only headset to support it is the PSVR2 a few months ago.

Actually you can get 3rd party PSVR2 adapter pretty cheap. That might be an cheap alternative to the Level1Tech USB-C combiner. Going to get one myself to try.

I had a similar issue, but I chose to solve it another way.

I connected both computers directly to the monitor and used lunar[0] to use a keyboard command to switch inputs. I then used a Deskhop[1][2] to share the KB and mouse between both computers.

It sounds awful, but in practice it was surprisingly nice. My monitor (LG Ultragear+) switches inputs fairly quickly. The process was something like this: hit the keyboard shortcut, then move the mouse off the left side of the screen. To go back, you reverse it: move the mouse off the right side of the screen and hit the keyboard shortcut.

[0]: https://lunar.fyi/

[1]: https://github.com/hrvach/deskhop

[2]: https://www.etsy.com/listing/1763041320/deskhop-jr-keyboard-...

Same issue, but instead I convert the USB-C signals of the laptop to HDMI/USB-A plus charging port with a cheap adapter. Then a KVM with HDMI/USB switching

Tesmart has a kvm with one usbc port but only uses hdmi as the graphics protocol.

https://www.tesmart.com/collections/for-4-pcs-1-monitor/prod...