You sound like me and your wife is my husband.
I don’t enjoy chores. For things I don’t enjoy doing I like to be as organised and efficient as possible to get it over and done with. It irritates me immensely if something be else makes extra work for me because they can’t do one small thing differently that takes no extra time. The dishwasher is only one example. My husbands thinks in the here and now (or not at all and just does) whilst I’d rather put more effort in early doors if it makes a big difference to the time and effort needed for the whole task.
This is where the similarities end because we’ve found a way around it.
I used to see it as him doing it on purpose or not caring about my thoughts and feelings, my husband really isn’t playing games and just doesn’t think at all. He’d accuse me of always thinking the worst and not respecting him.
So now, we both have tasks that are more important to us and do them from start to finish so there’s not overlap or teamwork required. Eg I do all the washing, drying, ironing and putting away because it’s easier for me to do it start to finish and less cause for conflict. He used to ‘help’ which meant washing was left to fester and then all required ironing. I love my husband, but not enough to not resent him for creating ironing. I loathe ironing!
He does the things that he finds important or that I don’t have a system for that makes much of a difference to the completion.
I think the key things are:
Do you actually like each other and are you both kind to each other?
Does your wife deliberately do things to wind you up?
If not could you appreciate that she’s just different to you and accept that.
Could you both specialise in different tasks to make the minimum st of what’s important to you both and limit the potential for conflict.
From what you’ve written though, it sounds as if neither of you like each other much and she just wants the convenience of staying together without being tied to you.