If I am doing less challenging, more routine coding, then I can just work all day with some music on and it's no problem. I've noticed when I am tackling tough problems I tend to spend a lot of my day not working. I go for a walk, I take a lot of breaks. When I am solving difficult technical problems I usually end up actually working about half the day, at most.

I feel like when each breakthrough occurs, I must let it sit for a while before I move on. It's like I can't touch it until some time has passed and things have settled.

Have you experienced something like this? Do you think this is laziness, or are we subconsciously solving problems as we appear to be acting lazy?

Yeah i experience the same thing, especially in the recent years. Guess it's a matter of age.

Beside difficult problems where we need to think a lot obviously, i also experience it on the other extreme, which is gluing a lot of working functionality together.
Current example is my terrain simulation. After working months on the building blocks like erosion, tectonic damage, modeling geometry from fluid particles, upscaling, etc., i'm currently in the process of making a pipeline to automatically process all those tasks in order.
This means i get very quick progress from almost no work. I may end up impressed and get the feeling i have already achieved enough for today. So i stop working for some time, run circles in the office and imagine where it could end up.
Or i end up disappointed if it does not work well, feel overwhelmed from the changes needed on multiple systems, panic all former work might be for nothing, and sit on the sofa to play some guitar instead working.

When i was young, i never needed a break, and i never did run out of motivation. But now it's no longer that easy all the time.

That downtime can be very productive for planning out the steps in the back of your mind. Have you noticed that when you do sit down to do it, it comes together pretty quickly?

If I experience some blocking issues that need pure brain power, then best I can do is to wait for another day. My brain usually comes along with some tackling points over night. It doesn't mean I can't sleep all night, I'm sleeping well but its like a sub-process floating around in the background and popping up to the front when its finished