A high quality contribution but an annoying error is present in my published article

It is probably best to do all of that. Contact the editor and ask if a correction can be published (letters to editor, ...). Put out a corrected version somewhere visible.

But also, don't obsess over it. Perfection is rarely attainable in an imperfect world with imperfect humans.

The sort of error you mention is very common, actually. Once you write something it is difficult for you to read it as incorrect. Often your mind "reads" what you think is supposed to be on the page rather than what is actually there. It is notoriously difficult for people to proofread their own work.

Ideally, the review process should have caught the inconsistency, but since it wasn't caught, others glossed over it also as immaterial to what your arguments are.

Since the asker said the in comments that the error is not related to the conclusions or results of the paper, the proper thing is to find something more important to work on. Unimportant errors do not need correction. Almost all papers have them.

Eternal rule of professional book proof-readers: no matter how hard one tries, an error will always remain.

...and this comes from Literature and Fiction. Factor in the added complexity of scientific writing...

...In short, do obsess over going the extra mile to deliver and proofread a paper to perfection. But don't obsess over the error that will stare you with a smirk after, in the published document.

Admittedly it takes some effort and practice to adopt this mindset.