Your son is normal.
Don't hold it against him. Or he will learn not to confide in you or express himself to you nor to trust you... and he will get emotionally pent up and learn to hide his feelings from you.
This is his body.
No matter how long a child is potty trained, they WILL have accidents. It is childhood. They are not absolutely perfect.
At this age, they are not even fully developed nor even their brain nor even their emotions.
ALL of my daughter's Teachers, from Preschool to Kindergarten to 1st Grade, ALL said UNANIMOUSLY that kids these ages have accidents. And if a kid has an accident, they do not make a big deal of it.
Kids who are 3, don't even have fully developed impulse control yet.
Per night time dryness, know that it does not occur even until 7 years old and even later sometimes. And night time dryness is completely different than day time pottying. It has to do with the physiological development of a child's brain/myelin nerve sheath/and organ coordination.
Your son is completely normal.
With my kids, I bought 4 waterproof bed pads from Amazon, and I put that directly under them, and therefore the sheets did not get soiled.
No biggie. My son is 6, and still wet at night and has a night diaper. My son's Teacher said normal. But parents don't want to admit that. But the Pediatrician says this is normal. But sure, he has been potty trained for years now. He still has accidents. Even at 7 years old, my daughter had a few accidents. I just explain to my kids that their body is not ready yet to be dry ALL night.
EVEN my kids' elementary school, in the Health Room, they stock extra clean clothing and undies for the kids that have accidents. They NEVER EVER, scold or shame or punish the kids for it. They are so young.
Your child is ONLY 3 years old.
Not a 12 year old.
Your expectations of him, needs to be age appropriate.
Otherwise, he will grow up, being so pressure filled and not able to be, himself. A child needs to be himself... to know himself and his feelings... that is how a child becomes self-assured and happy.
Kids are not robots.
They need to vent, they do have accidents, they need to know that they have a soft place to fall when sad or grumpy, they need to be allowed to know themselves and their emotions.
He is only 3.
Controlling a child so much... does not mean they will be better than another child. And some kids who have lots of freedom to express themselves, grow up very well too.
High control of a child, does not make them robotic. Nor perfect.
Some people are good rule followers... but, they are emotionally or mentally immature. It depends on how they are nurtured or not.
I know a girl, who is now a Teen. 16. All her life, her parents ruled her with a tight leash. They were SO proud of it! She was always overshadowed. By them. What a goody two shoes she was and a great obedient student. Everyone raved about her! BUT, behind their backs, everyone would say that that poor girl was just a robot... and just doing things because her parents were so so controlling. It was like that girl couldn't even have her own thoughts or ideas. Her parents always knew better. BUT they did NOT know... their own child. They only knew the stereotype "child" they wanted and they raised her like that. Well now... she is just going all out, defying THEM. Because, she can't stand it anymore. The parents now, have a hard time with her. Because... They do NOT even know, her. They never really knew her anyway. They only knew what they... wanted. Not what or who their child was and is.
It is really sad. She is so... much, trying to reject them. And she resents them. She is now, being herself. But yes, she is still an "angel." She's a good kid... but is just being herself now. And her parents are aghast. But they were the one's who did not "allow" her, to be herself.
The girl, even vented to me once, saying "My parents pressure me SO much.... I can't even talk to them about anything unless its what THEY want me to say. I have to be so perfect. They are lucky I am smart. What if I was dumb? They couldn't handle it."