Your son sounds similar to my daughter at that age. Since he is very active, he will need large amounts of food. If he is slim and not purging, he is not overeating. That doesn't mean there isn't an issue though.
Due to early lie experiences, my daughter used to panic if she did not get food instantly when hungry. We used to have our family rules at the fridge and one was "we always have enough food" to increase her feeling of safety.
She could eat as much as she liked for dinner times, so she would often have 3 large portions. If she looked full but wanted more, we would gently say: "Are you sure you need more food? Feel into your tummy. How does it feel?" to increase her awareness. She would then often just take one more bean, just to be able to chew a bit more. Chewing calms her down.
We did use to regulate her snacks, but they were still large. Just to give you an idea: In the afternoon she would usually have an apple, a banana, 4 rice cakes, a pepper, carrots and a small sweetie, eg. a rock.
We had a rhythm of meal, snack, meal, snack, meal with about 2 hours in between and tried to keep meal times calm (no tv). Had we not done this, my daughter would have eaten non-stop. We also never had a snack box.
The constant asking and talking about food is very familiar to me. My daughter memorises people by the food we have had with them. She knows there will always be food, but if she gets very hungry her survival brain still takes over. She very often chews gum or on a "chewie" (you can get them on Amazon) in order to calm down her anxiety. When she was little, I always had gum on me.
So we have tried to give her a sense of how she could be eating in the long run and tried to increase her awareness for when she is full. We have also tried hard to keep eating fun and to see it as something that is immensely enjoyable.
We have always been positive about food when talking to others. Other mums very often commented after play dates on how much my girls ate and I used to respond proudly along the lines of "yes, we all eat a lot!". At home we have conversations about how it isn't fun to eat with picky eaters, so my daughters can feel good about their eating behaviours and not ashamed - and because that is how we feel.
My daughter is 14 now and still working on improving her ability to distinguish between "I am hungry" and "I am worried/scared/etc", which is at the root of the problem.
I am pretty certain, OP, that you are not causing this problem. To me it sounds as some other posters might not be adopters and don't know about the effects of early trauma on the brain.