I'd start by asking him if he realises how hypocritical he is sounding. He can't feed the baby dinner because he is much more tired than you because he works out the home amd you have it easy looking after kids. But on the other hand, doing a bit of childcare is so tiring that he can't possibly do it after a day at work, as its just too much. If it was that easy that being a sahp was a piece of piss, it would be no problem to help out. If it was that hard that doing 20 min would finish him off, then he should be helping.
Would he take the attitude that he does at home at work? Say he was working on a project but it wasn't his main work and it was someone else's full time role. And every time they asked him to do some work (which was part of his normal role, for a few hours a week) he said 'but you're the project lead! I'm only partly responsible here, so you should do everything by default! Why aren't you being more grateful to me? This project is so easy, you've got it good working on it full time...but spending half an hour on it will be too difficult for me, I'm so tired from my other projects'. I doubt it, he would come across as difficult, petty, point scoring, unhelpful and insulting to the other persons role.
I don't know what he thought having kids would be like but most people understand that being a parent, even if you work full time, means that when you're at home you have to parent. It's not fair that you work 24 hours a day, getting up in the night, continuing at the weekend, while he just works 9-5 and gets the rest of the time off by default unless you beg him, at which point he will begrudgingly 'help while belittling your efforts.
I'd be telling him you do appreciate everything he does but it doesn't feel like jt goes both ways. You feel unappreciated. How would he feel if you made it clear his job was so easy that it was pretty much a holiday and anyone could do it. Why does he think it's fair that because you're the primary carer when he is not here, that you should be the sole carer by default when you're both there. Why does he think it's fair that you work 24 hours a day 7 days a week and he does 9 til 5 on 5 days. If he is constantly too tired and stressed that he can't do normal adult and parent stuff outside of work, what is he doing to address this, as the majority of working parents manage to do do stuff with their kids when they get home.
I'd be asking him what he thinks should change as having sole responsibility for parenting all thr time is making you ill. I'd tell him I'm thinking of 3 options:
He starts respecting your role and doing his share of parenting and house stuff at evenings and weekends, or
He supports you improving your mental health and getting back into work. This means you will have to share everything outside work - pick ups drop offs sick days, mental load (sorting hair cuts, clothes, shoes, meal prep), parenting, house chores, as you will no longer be the primary parent
If he can't agree to either of these you split as the respect has gone, and at least you will get a break of every other weekend, or if he wants 50 50 care you can use this time to retain and get on with a new job / life