Strange, I've seen quite a few merchants that do the card surcharge thing, and no one seems to complain.

The Supreme Court settled it in 2017 actually - surcharges are fine now:

https://archive.is/eYB5W

They basically said a surcharge for credit is effectively the same thing as a discount for cash, and because of freedom of speech, merchants are free to communicate the difference to their customers either way.

But is a payment processor required to process charges from a vendor stating they have a surcharge?

only took them a few decades

I've seen cash stations offer a cash discount. It was always less than my credit card's gas reward and required me to go inside the station to pay.

Gas stations do the cash discount for a particular reason - to get you inside the building where you might buy profitable convenience-store items, which you won't if you just stay at the pump. (Though yes, the differential might be less than the kickback from a card rewards program.)

Ive seen restaurants do as much as 4% off for cash.