There are solutions to wifi using an ethernet bridge device (not ideal). Windows 11 can still do WoL, so I'm unsure what the other comment is about.
If you're in the OS, both of those solutions are easy. The machine can be in a suspended or powered off state. Presumably you could WoL it, remote in, then do whatever you wish.
A remote shutdown sounds like a return of Back Orifice.
So hard power off = shutdown, reset = restart?