There is no evidence and it is absolutely impossible to probe there is any pain at all
It is possible to do veterinary studies to look at brain activity during euthanization and determine if the animal feels pain in the process.
I read one such study done on turkeys during the slaughter process. I think that similar studies would have had to be performed before the FDA would approve the euthanization drugs.
My only evidence, one way or another, is five or six general anesthesia operations I’ve had in the last 40 or so years. No pain each time and just like riding a time machine.