I've recently gone for surgery for the first time in my life, and was treated with the standard cocktail of fentanyl+propofol for anaesthesia, making it also my first time on an opioid (and a strong one at that). The way it works is that you get the fentanyl first, and then shortly after the propofol.

It wasn't exactly pleasant. In fact in the time before propofol kicked me out I even said out loud something to the tune of "Hmm, so that's what opioids are like. I do not like them". It was exactly as the OP describes, you just kind of cease to exist / reduce your presence, if that makes any sense. It was more like the 2001 scene when HAL says that "my mind is going, I can feel it".