OP I'm quite close to your DH in this scenario in a lot of ways. I keep looking into getting an adult diagnosis of ADHD, but basically: I have chaotic tendencies and struggle, genuinely, with a lot of things that fall under executive function. It also effects me hugely in work but I'm at a level where basically I can just about scrape by (unfortunately senior enough that nobody is checking my work day-to-day or even week-to-week and I can pull things together for annual reports etc when I have to)
We both work full-time, currently one child in nursery, and we have a cleaner but I would say DH does 70% of day-to-day housework. He cooks most meals, he does most cleaning and tidying. Our house, however, is often very messy: I think we both have lower standards than you would. Where it differs is I actually do the planning/ 'wife work' because I have basically been socialised into thinking its important and he doesn't care. So, I'll buy the Christmas cards and look into swimming classes, though he might take her, I'll do the annual bills, if we move/need to switch supplier I'll take charge of that, but we have a rule about not engaging in any trial periods for things because we both never cancel them and everything is set up to renew on direct debit in case. I deal with the cleaner, and I do most of the 'people' interaction because he finds it difficult. I buy all DDs clothes, and do the shopping.
DH has in a lot of ways 'trained' me, which is something I always see people recommending against and I understand that in the normal way of things. But I think he recognises, very well, where I'm genuinely struggling or taking the piss a bit. So, if a room is incredibly messy, I am genuinely overwhelmed by it and don't know where to start. He will give me a task, tell me to only do that task, finish it, and come back to him and he'll give me a new one. So: room if full of toys and mess and chaos, take all the clothes in the room, remove them to the laundry basket, don't deviate from that task then come back when its done. Obviously this isn't every day, but actually he's done it so much that it has really helped me know how to go about it.
The other thing is: we have a principle of both contributing as much as we can, how we can. So, the fact your DH 'can't' cook is a bit ridiculous. I actually can cook, but I am clumsy and slow with chopping vegetables and it genuinely takes me longer, so it makes more sense for him to do most of it. But pretty much everyone 'can' cook if they put any effort into it, even if it takes them longer. But it sounds like either you or your DH have thrown your hands up a bit around the areas he struggles to contribute. Some of them, he needs to get outside his comfort zone. Others, I would actually suggest you reduce your effort in some areas to make up for more efforts in ones he'll struggle with.
So: you're frustrated you need to remind him about half term. If that's something you genuinely think he's bad at, maybe you need to accept that, but not accept things like you cooking every day: he has more time, he can figure that out more. If you have more space from the tasks he can do, but chooses not to, then it won't feel as much of a burden to have to step up on the areas he struggles with.
I actually do a lot of the planning, thinking, looking ahead stuff: largely because I know I'll be rubbish at doing it last minute. On balance, DH and I think we both contribute equally to keeping our family running, and we're both giving as much as we can. He's an incredibly hard working 'do-er' but there are things he hates doing and thankfully they're things I'm ok at so I take up the slack there. I think its worth focusing more on that: he's working part time, he can pick up more of the slack, but sadly he's probably genuinely not best suited to that around some of the executive function areas, or he needs more support there. You need to both do a bit of thinking about what areas he can more easily step up in to even out the load.