Back in 2004 I used hardware -- an Xkeys Programmable Keypad along with a KVM (5+ Physical PCs)
https://xkeys.com/xkeys/keys.html

Example: one keypad button would send
"scroll-lock scroll-lock 2 1"
"scroll-lock scroll-lock 3 1"
"scroll-lock scroll-lock 4 1"
"scroll-lock scroll-lock 5 1"

which would "go" to computer 2 and "press" 1, computer 3 and press 1, etc.

Basic and slow but it worked.

I'm sure people will come out with something. Necessity is the mother of invention and all that.