Author here :) Fortunately, I mostly don't idly browse the internet on my computer - that habit is attached to my phone, which I just leave in the other room :) But in general, yes, if I need a break, I check off what I'm currently doing, write down "break", and then take a break, and check that off when I'm done. But my experience is that it's probably best to keep your breaks physically separated from your workspace if possible so that when you sit down to work it feels like "work time".
I ended up with the same approach. I used to do my idle browsing on both, the PC and the phone. In an earlier bout of productivity (many moons ago) I blocked all the usual suspects on my PC. That was several years (and PCs) ago - but there's now never an inclination to hop over to those sites on the PC and the "missing out" feeling isn't there since I can check 'em on the phone (later). For whatever reason, it feels more like goofing off when I'm on the phone, so there's a slight aversion to doing that during the regular day.