I've seen the gamut of answers to this question over the years. To a large degree, I think it's just whatever works for you and your household.
For us, I would wake him as I was going to bed for the night and have him go one more time (usually around 11 pm). Bedtime was 8:00. He never woke up fully enough to even remember, but I'd walk him (sometimes carry him, b/c he was dead weight) to the bathroom in the hall just outside his bedroom, and stand him up... he'd potty, flush and he was back in bed and sound asleep 30 seconds later.
This went on until he was probably 5 or 6. It just wasn't worth it to me to wash sheets every single day. And this was a while ago and the larger overnight pull ups were just coming into "vogue". I have no idea if this practice prolonged his maturing into being able to wake at night (or hold it all night). He was an extremely deep sleeper. Sleep talker and sometimes walker, as well.
Around age 7 I mostly discontinued with the "dream potty break" routine, and just made sure he went the absolute last thing before he crawled into bed. After bedtime stories even. He'd go potty one last time while I tucked his sister in, and then when I was done with her, he was ready to be tucked.
It wasn't until age 9 or so that he finally stopped having the odd jag of wetting the bed here or there. Until then he would have long periods of complete dryness at night (a few months or so) and then he'd wet the bed 3 nights in one week. Then long period of time completely dry, and then 2 nights in a row of wetting the bed. Then every other night the next week. Then dry for months. Etc.
Some of it, I'm sure, was physical growth. Not sure exactly how it all worked, but eventually he outgrew it.
His sister (3 years younger) never had this issue at all. She was dry overnight from before age 3, and has had less than 5 overnight accidents (notably, these were at times when she fell asleep in the car and was brought into the house in the wee hours and dumped directly into bed without a potty stop, or something like that where she fell asleep early and I decided to risk not waking her up).
She also doesn't sleep talk or sleep walk. And has no allergies (which son does).
I don't know if any of those other things are connected, but I know that when son began getting allergy treatments (shots), the number of nights I've heard him sleep talking dramatically reduced. He finished his treatment plan a few months ago (over 4 years of it) and I can't remember the last time I heard him talking in his sleep. He also wakes up a LOT easier in the mornings now than he used to.
Before, I had to physically jostle him, speak to him loudly, and then come back and do it again at least twice, before he was actually awake enough to make any conscious decisions about getting up. He wouldn't hear a loud alarm clock in his room--that would wake US up at the other end of the house. Now, he often will hear me open his door in the mornings, and looks at me before I touch his foot. No jostling required. Only ONE "wake up" needed.
Try not to stress. If it works for you to keep him in overnight pull-ups, go for it. I know plenty of kids who have gone that route. They don't go to college in them. And at age 4, MOST boys have overnight wetting problems, I think.
Good luck. I know it can be frustrating.
Be sure when you decide to ditch the pull-ups that you teach your son what to do with wet garments/bedding if an accident should occur during the night. You don't want him to lie there wet b/c he doesn't know what to do and doesn't want to have to come wake you up.
I just had my son put the wet things in the bathtub, wash with a washcloth, and put on dry undies. He had a full size bed, so usually the other side was still dry and he could put a towel down if needed, or he sometimes would get a blanket and sleep on the floor (carpeted).
No biggie. No shaming. No fussing. It's just the way it is sometimes. Teach him how to handle it so you don't discover the bedsheets and stinky PJ's and underwear at bedtime the next night. (been there, done that)
He's a little young yet, for all that, but if the situation continues, that's an option for dealing with it while you are patiently waiting for his body to mature.
No need for a doctor's involvement until at least age 7 or maybe 8, if you see NO improvement by then.