If I can make a suggestion, I would suggest you let your DS have school food under a strict condition:
you credit a certain amount per day or per week onto his account (e.g £4/£20, or whatever you think suitable) and he has to choose wisely and budget. And, you will sit with him and both look through the listing of what he has bought, and have a discussion about it. Every day, or weekly, or whatever suits.
Then you can figure something that suits you both, without clashing, without stealing, and encouraging healthy choices. If he's actually hungry and £4 isn't enough, he can take in some fruit, a granola bar, something home made.....he could buy a snack and take in a lunch, or vice versa.
And I would sort of apply the criteria to the older brother, as in looking at his choices and all having an open conversation about food choices, eating only when actually hungry, making good choices.
How does that sound?
FWIW, my DS1 is 14, 6 foot 1 and very skinny. DS2 is 10, about 5 foot (quite tall but also a stocky build) and has a layer on him. I do try to guide choices for DS2, where I can, and he is on a few 'sugar swaps' but it is low key. I will let him choose his food in senior school, but I will keep a closer eye on what he's buying. If it's doughnuts and chips, there will be a discussion about, for example, a doughnut once a week, chips max of twice; if he has pizza then he needs to reduce the chips. If hungry at break time get a hot wrap or a sandwich rather than crisps or muffins. Encourage the 'meal of the day' which at our school tends to be meat and two veg, or a stir fry, or a curry, shepherds pie with green beans, that sort of thing.
It's not easy, and I can see you want the best for your son. I also think you've had a bit of a bashing here. I do believe that if you let him have a bit of autonomy it will be ok.....[and bear in mind that teen and pre-teen boys really do eat a lot compared to the average adult woman!]