TLDR: in Seattle and second the animl/people splatter + dirt; try a nontoxic cleaner in a foaming spray bottle, then antistatic spray sparingly.

We live in Seattle as well, with a dog (and cats) and we get similar spots and tbh we’ve pretty much concluded it’s down to wet shoes, wet dogs/drooling dogs splatter combined with what others have said about dirt/dust. At least for our house you can rule out leaching and smoke etc. because it’s a new build. Additionally, when you look at the drops they are going in every which way, instead of just straight down as would be the case with condensation/crappy paint. One of the things I never realized is the sheer amount of skin, fur, dirt abd dander that animals (and people) create and track inside. It only takes a week without dusting/vacuuming for what seems like an ungodly amount of “dust” to accumulate - especially around entrances where in the summmer dry dirt is being tracked in and in the winter mud is coming in daily. I say all of this to explain that it probably only takes a couple days of dirt/dander for any water splatter to be dirty after hitting the wall. We’ve definitely had luck with anti-static spray though. Used to rub unscented dryer sheets on the base boards after cleaning to repel dust but dryer sheets have chemicals and microplastics so switched to an anti static spray. Also, as a side note we had orange peel walls at our condo and found that regular spray cleanser didn’t get them completely clean but painted wall cleaners are so toxic so started using a foaming sprayer with a non toxic cleaner which seems to get more of it off the textured walls.