@pastacaring my heart goes out to you. I can empathise with how positive it feels as a parent when your child has a goal which gives them motivation and drive.
Then to find that this goal may be unobtainable is a horrible blow.
I also empathise with how helpless this makes us feel as parents. It is so so natural to want to fix things for our children. But, I think maybe your son would be better served by you listening and accepting that this isn't ideal and that it is understandable that he is upset or angry.
I realise that typing this here is a lot harder than actually doing it IRL though.
My son had a period of poor MH during lockdown, along with some anxiety. I was really worried about him, as were his teachers. I reached out to Camhs for help (and like you found it to be not very helpful).
I think I did the right thing. I couldn't have held off incase it affected his future. This is the same reason as you did it- out of love, and because we do what we think is best at any one time.
I think the advice on this thread to follow it up with the recruiters, and to try to distill what it is about the army that appeals to your son is great.
Sending in Mumsnetty hugs.