I think if there was a phrase I'd like to see banned (or at least given a rest!) is 'formula is not poison' :( :(
No one coming on here worried and upset about giving formula thinks formula is 'poison', or 'dirty ditch water', or anything else (obviously it is none of these things!).
Gosh....I know people are trying to be kind, but when mothers are distressed about giving formula, they already know they are not giving 'poison', but they are upset that it's not breastmilk. It's normal to be disappointed and sad when the desire to fully bf does not work out, and it's normal to be disappointed and sad when breastmilk does not seem to be doing the job of nourishing the baby. It's not normal to be as devastated and in floods of tears and full of anxiety about it and depressed - and this is what needs addressing :( :( ...rather than any idea of what formula actually is.
smk, you know you have been doing, and continue to do, the very best for your little boy. Your reaction to giving formula is linked with your anxiety and other aspects of your mental health, your stress and the fact you are not enjoying life at the moment....and I have no idea if this is because you have very high standards for yourself and you feel like a failure if you don't meet them, or if it's to do with other background stresses and worries.
Giving formula may be the right decision for you and your ds, because of all the things you describe in your post, and there is nothing to feel bad about (which you know in your heart is true) - but if you can, focus on your feelings and your day to day challenges of coping with being a mum and the relationships you're forging....rather than what goes into his tum! I can't remember if you are already getting help with all that side of things but you could ask your HV if there is any specific infant mental health service in your area which uses gentle therapeutic techniques to help you, and where you attend with your baby.