DP is completely incompetent

Did you write his CV? Did you go to job interviews with him holding his hand and passing cards with what he needed to say?

Do you have to manage him like a toddler for him to get ready and to work in the morning?

In the likely event all the above are a no, and he's a normally functioning adult, he's just being a lazy arse and has no excuse whatsoever.

As someone with physical health issues, crippling anxiety and who likely has ASD and ADHD and manages to work, parent healthy happy kids , run a home and (mostly) keep appointments and manage tradesmen and the like… I would suggest that you’re allowing this uselessness to perpetuate. It’s easier to let things go and do it ourselves sometimes but then you create the monster that is an adult who can’t ‘adult’. So put your foot down, get a chalkboard and explicitly list the tasks needed to be done and nag until you form the habit of him looking, doing and completing each task. I assure you that while some of us need aides like lists and alarms to function we can, when required to, actually do it.

This. Such a good ploy, my ex h was an expert.
As a pp said, tell him to do the shopping and he cooks meals for the family with whatever he buys.
Or give him the cleaning to do on a Saturday, all of it, and go out with dc for the day.

This. I have ADHD and am a single parent - yes, sometimes my house is disorganised, but I am capable of running a household/medical appointments/bills with little effort.

What you are describing OP is learned helplessness - check out Bridging The Gap on FB. These are men who either are incompetent because they can't do them (cooking, washing) or be bothered and see it as a woman's responsibility, or weaponised incompetence when they can very well do all the tasks themselves and choose to let you do them instead.

First thing I'd do is probably bin him off tbh

I can't imagine how you forced yourself to procreate with such a waste of space. Incompetence is as unattractive as stupidity and I can't tolerate either trait. Just dump him already and he can go off and be useless on his own without it bothering you.

You're wrestling with the modern sharp end of the gender war. He thinks all he has to do is ho to work and the rest is up to you.

I'd take the advice above. Do the money tasks and ask him to do other stuff.

Doesn't help with the mindshare aspect of it.

Do you still fancy him??

I would think this too.

if he’s a lazy arse you would be able to tell with the attitude that comes with it. If he seems willing but just a bit shite I think it’s not lack of effort

I have ADHD and am a single mum with complex health conditions and I still manage to make sure Dd has everything, run the whole house, life admin, work and attend medical appointments. Men are always let off so easily with this stuff.

He CAN do it op, he just can’t be fucked and know you’ll pick up the slack. I bet anything he’s fine at work and manages there ok.

I'm with @Polari. Rather than trying to micromanage him and getting frustrated, ask him to do a task and then genuinely leave him to it.

For example it's his turn to change the bin. Once you've agreed that, do NOT, whatever you do, fold and change the bin yourself. Leave it for him to change, even if it's piled up, overflowing and stinking. Just hold your nerve until it finally gets irriatting enough for him to change it. He won't make the same mistake again.

Likewise, with dinner. Pick an evening when your kids are out / with grandparents / having tea elsewhere for this one. Agree with your husband that he's going to shop and cook dinner. Then just let him get on with it. If he comes back without food, or he goes hungry? Fine. Then dinner does not get made (make sure you eat a big lunch or have some secret snacks for yourself - no need to endure a rumbling tummy).

Or, say, cleaning the toilet. You need a strong stomach or nerve for this one. Once you've agreed that its his turn to clean the loo, do not, whatever you do, cave and clean it. Hold your nose and put up with it. He will clean it. Eventually. And it'll be such an unpleasant job that he won't let it slide for so long again.

Consequences. He'll change when he recognises that they exist. But at the moment, you just keep bailing him out, and he gets to keep playing the martyr.

It's weaponised incompetence

What does he do for work??

I bet he's competent there!

He's NOT a man, he's a child.

Do you want to be involved with a child?

Just move on, someone with a weird Mothering fetish will look after him once you're gone.

He sounds like a lazy arse. It's called learned helplessness and it works. He is useless and you pick up all the slack.

Has he any diagnoses? Sounds potentially ADHD-ish from what you've described.

Has your dp always been incompetent or did it start with living together or dc arriving?

I think anything big financially then take control.
However shopping, cooking etc just leave him to it.
Tell him to go to the supermarket and whatever he buys then he can cook with it.
Do this until he realises you will not bail him out.
The dc will be fine.