Slightly different here, we're both dx, him ASD and me ASD/ADD... him through the NHS channels and me privately, because it makes no odds to me, I can't have any medical treatment anyway, he potentially might in the future.
I do let a lot slide.
I have to point out jobs that need doing, he won't see them.
I come up (with his input) ways to work around stuff - for example, written lists, not giving verbal instructions more than two items long.
He will always be easily distracted though, I have spent the better part of 40 years masking and working out my own workarounds, as I have had to. He, until he lived with me a/had no idea he was ASD and b/lived with his parents so he just had to go to work, come home, keep his own room tidy, no other responsibilities!
So when it comes to time management, I understand and im well practiced at say, swapping laundry from washer to dryer whilst the kettle boils, doing the washing up/wiping surfaces down whilst food cooks.
He will just sit and doom scroll on his phone whilst waiting, he can't multitask like that.
His natural understanding of time passing is not the same as mine either - in his mind, the time he spends thinking about doing a job is added to the time spent doing the job. He feels (genuinely I am sure) that he spends a minute or two having a sit down before doing something and is shocked to find out he has been sat for half an hour or an hour in reality.
This does lead to friction as theres often a lot to do, I am dependent on him doing may physical tasks as he is my carer and I can't do them!
You can see it in his responses to conversation too, where a NT person would have a pause of a few seconds, if that, before responding, DP will respond anywhere from a minute to five minutes later, often if theres other people around the conversation has long moved on and his response is now irrelevant which then makes things awkward and clumsy.
Sometimes, he has thought of his answer but not given it and is unaware of this, and does not make a noise, no hmm, umm, general 'I have heard you and I am thinking' type response either. Then I tend to nag, and then he gets cross as he thinks he has responded... and hasn't!
One I have got up to speed with and no longer throws me at all, but does others, is the random comments relating to something we were talking about earlier (hours or even days!), which pop up prompted by something... anything.. or nothing at all, vaguely linked. I can usually get on track with where his mind was in a few seconds now but it used to take a while!
Some of it is infuriating and sometimes he is genuinely being a lazy fuck (as I can be too!) but mostly it isn't intentional and we have muddled along for the last 19 years without murdering one another!!