You will laugh, but when I do the dishes, I solve sooooo many problems in my head and can't wait to get back on the keyboard and apply those solutions; it works wonders for me!
In my opinion, when I finally give up and go for a walk/chore, my brain is so bored by the boring task that it stops procrastinating and actually focuses on the problem.
Also, when I do other type of chores in my garden helps quite a lot!
But I've found as often the obvious brilliant solution while I'm away from the problem doesn't survive 5 minutes contact with all the constraints I forgot about while I was away from it.
Basically I think we count the hits, and discount the grind necessary to produce them.
Distance might help me see something I had missed, but that is an exceeding rarity. If getting away for a moment was magic we'd be in a nicer place. Everybody poops. Fewer put in effort.
Jokes aside - completely agree, pretty much the same for me.
Another effective hack is to verbally talk about the problem to someone else. That seems to change how the brain processes things and that new perspectives can find the answers internalizing could not.