I desperately want to do this type of walking, but I live in a major city. There’s always something to distract me, which is great for boredom perhaps, but ruins any sense of zen or reflection. I would say half of every walk involves people yelling, loud vehicles, and louder music. Noise-cancelling headphones are only useful for distraction through podcasts and music, not for decompressing. I’m starting to wonder if the solution, the sad solution, is to walk on a treadmill at a gym during off-peak hours.
I am also not too satisfied by this problem. Newport says city walking increases decision fatigue instead of decreasing it. It seems like another point against urban environments. I still walk to and through city parks and I feel it helps me, but I take the same designed route every time to reduce decision fatigue. I think it still helps.
Have you considered earplugs? The firearms community have some pretty great ones which are readable and fit really well. Check out Axil x30i for example.
I find thunderstorm noises superior to white/coloured noise - because it's a natural sound the brain filters it out, and obtrustive noises are camouflaged within it, and filtered out too. So the loudness required is less than the loudness needed for white/coloured noise to be effective.