Tell me, how does the start button on the PC case? It is a switching power supply or what?
No. Motherboard all the time under power. Button closes the contact on the motherboard, feeding enable signal, the logic programmed in all motherboards that support ACPI. In ancient motherboard (until the 2000s) the power button was not a toggle switch - it is switched power.
I want to make a run of machines without physical presence of a button on multiple machines.
Read wake-on-LAN - now it's built 99% of the motherboards, don't need to do anything physically simple to configure.