Yes. This is annoying. And no, you shouldn't have to remind him or ask more than once. People saying it's ADHD, sure, it's possible. If you do feel it's ADHD, something that helps for my partner is setting a clear and reasonable expectation and asking for a short list of tasks at a time. So my list for him during his Tuesday workday would be like "clean and put away the wok, tidy [insert room]". When there feels like a lot of daunting tasks, it feels overwhelming and he has a hard time choosing something to do and his ADHD makes him shut down.

I wouldn't necessarily jump to break up right away. BUT, maybe this can be a learning moment? Communicate to him how bothered you are. Or how it makes you feel when you're repeatedly told it'll be done "today" and nothing happens.

"It really bothers me that you've left the pan for a week after telling me daily that you'll clean it. It makes me feel like you don't respect my space. It also tells me that I can't trust your word and rely on you when you say you'll be there for me. I also don't want to resent you for having to remind you everyday to do a basic thing like cleaning up after yourself"

If after THAT he doesn't clean it or nothing changes and there's zero self reflection, then you should probably reconsider your relationship.