These people going for walks, taking showers, napping and solving problems: I don’t have this experience. Instead for me it is using pen and paper that does it for me. And it seems more efficient to have a computer nearby to browse code or docs while I do it. Breaks are helpful for maintaining energy but not for eurekas. But I agree that if walks make you more productive and you are thinking about work then that is actual work.
I think the key is being able to genuinely relax from focusing on the problem to help your thinking. To allow an opportunity for those competing thoughts that aren't making it to your awareness because they are beaten by whatever train of thought you are stuck on. Little rituals like taking a shower (or sitting on the toilet is a popular one) distract you so you can relax. Or they should. If it isn't working for you maybe you are too good as staying focused and aren't getting the benefit from relaxing. Thinking about work while walking would defeat the purpose.
For me it is the reverse. My best creative time is the sauna, followed by the shower, and lying in bed in third position. Pen and paper work great for fleshing out stuff, but not for the original insights. Once we get to the keyboard and screen that is the implementation of ideas already formed elsewhere.
This is not a straight cascade, but different phases influencing each other. I also want to point out that its not a value statement. All phases have their own merit, and all of them pose their own challenges.
At least for me, doing without any of them will grind creative productivity to a halt.
