In the latest episode we get to see the outright answer for this for Cain / Kinger

As you can see, the circus (managed by Cain the AI) uses an oldschool Windows OS, looks to be 98?
Kinger then uses CMD to ssh into some bash shell, I dunno if we get much view of what kind of OS it is, but it appears to be possibly a systemd flavor?
We also get to see that the circus was programmed in Lisp in the latest 90s, which sounds about right
Based on what we know about the laws of how the circus works, these indicate a manifestation of how these 2 characters mentally work with OSes.
Cain works in windows 98.
Kinger on the other hand visualizes stuff with linux!
Hmmm, that might be true, or specifically the the whole circus env is one? It does say
kinger@circusas his target, interesting!