Not eating? 5 y/o.

My son is 5 years old and for awhile now he has been having "trouble" eating. Not necessarily trouble he just wont eat. A lot of the times we are believing its a game to him. We do not force feed him, we ask him when he wants to eat and his 1 y/o sister is on a food schedule so everytime shes having a meal we ask "hey bud you want lunch?" and he says no.. However we are running into now that he is BINGE eating at night time because he is refusing to eat during the day. When I make dinner we make him a plate and he'll sit and cry he doesnt want food, we usually just make him sit with us and if he wants to pick at it then he can but as a family dinner we'd prefer him be there with us. anyways: back to the binge eating around 10:30-11pm he'll want food. He will not eat fruits and veggies at all, not even one. He will make himself vomit (literally, shoves his hands down his throat) if we even put a veggie or fruit on the plate. So, he'll have a bag of chips, fruit snack and 13 pizza rolls... yes, 13.. and still want more. Usually we cut the limit because thats way too much food for a 5 y/o at 11 at night. Ive spoken to the doctor and he recommended therapy which he has been in for a year now (3 different therapist so far) and all of them just keep saying just put food on a plate and make him sit there while we eat and see if he'll pick at it (he never does and it always goes to waste) this has been a thing since he was 3 years old. Its to the point now he is losing weight and refusing protein shakes/ refusing vitamins. I have to crush them up or put them in a fruit snack pouch to mimic a fruit snack to get him to actually take them. Im extremely overwhelmed Im worried and I have no idea whT to do to try and get him to actually eat.