In PCI Express slot there is indeed a standby power (+3.3 V) pin and WAKE# signal pin, but it works differently than the power button.

https://en.wikipedia.org/wiki/PCI_Express#Pinout

The main difference is that WAKE# signal only restores power to the system but it does not change the system's power state, after using it the card needs to send an interrupt to the motherboard to properly wake it up. Power button does both things.