Finding this so interesting as 1) I'm exactly the same as you OP, and 2) generally the threads I see are the other way around - I.e. women getting really annoyed that men don't pull their weight.
I think it's a tough one, because on the one hand you and your partner have opposite styles of living that would make you happy.
You're not being untidy just to piss him off, you simply don't notice it and would probably rather a relaxed approach where (for instance) you can sit and enjoy your dinner, and chill for a bit, without thinking about plates. It's not that you won't tidy, you just don't always need to do it straight away.
By that logic it's two different ways of life and you should compromise and meet in the middle. E.g. plates always done before bed, but not necessarily right after dinner.
On the other hand from your OH's perspective, it is frustrating when you consistently tell a partner something is important to you and they keep not doing it, so you have to.
That would wind anyone up regardless of what was being discussed. So that's hard.
But I do think you're right in that "tidy people always win", and I think that's because his need for things to be tidy is generally seen as good, whereas your untidiness is generally seen as lazy / bad.
Perhaps the trick is to reframe it so you're both talking about your needs.
To be happy - he needs everything to be clean and tidy. But equally for you to be happy, sometimes you need to just chill out for a bit and put the tidying off. They're competing needs and equally valid. Therefore a compromise (as above) is required. And maybe take it from there. Perhaps there are other non-tidying chores you enjoy / care more about that you can take on to redress the balance a bit.
I'm v. lucky (in this at least) in that while my OH is a neat freak and I'm a bit of a slob he acknowledges that I really do try, and seems to actually enjoy the tidying, so we divide the labour so it works for us both.
Frankly I prefer the house a little bit "lived in" but I don't object to him cleaning like a maniac (and the fact I can't find anything once he's tidied) and he doesn't object to me leaving my shoes everywhere.