That sounds so stressful. My autistic son went through similar issues.
We chatted, very gently, about what food does for us - why we need protein, vitamins, fats, carbs for energy, strength and to improve our mood. I'd ask if there were any things in each food group that he thought he might be able to manage. I'd tell him about the foods that boost our mood - pink grapefruit juice, blue cheese, walnuts (most nuts and seeds) and see if he fancied any of these.
He too would eat two mouthfuls and then just stop, so I made those mouthfuls as calorie dense as possible. Banana bread or brownies made with almond flour and lots of eggs. Two mouthfuls of cake have about 4 times the calories of two mouthfuls of bread. I always tossed veg in melted butter, pasta in olive oil, so even if he ate a couple of mouthfuls, they were more calorie dense.
If he can face drinks, try banana milkshake with vanilla protein powder, some liquid multivitamin drops and a tablespoon of cream whizzed up together. Maybe a teaspoon of peanut butter or almond butter too, if he will tolerate it. Give him a small glass of it, not a daunting huge milkshake glass. If he can face soup, stir in some single cream.
Don't force things. But if he does eat a bit, ask if it has helped him feel a bit more alert in any way.
The resistance to medication is tricky, because, ironically, some antidepressants massively increase your appetite. That happened to DS when he finally started on them.
I really feel for you. It is so distressing.