I think it stems mostly from the fact that the work we do (and our way of life generally) is boring to the point of being tiresome for the brain.

Your brain gets tired of work and boredom, but it still strives to alleviate the boredom. One of the easiest things you can do is read news and bite sized portions of cool stuff. It triggers emotions especially in minds like ours. The only easier thing I know is watching TV (YouTube) but it's less rewarding for me so I only choose it when I'm too tired to read but not tired enough to sleep.

I think what's most important is that reading internet the way we do it when we feel the urge is worthless. You might think you learn stuff that can be useful for you in the future, but for each thing that marvelously hits the spot before you forget it (and that's like one for each 1000 things you've read) there are 50 things that you learn as you go when you need them. You might as well learn 51 then.

So you should be aware of confirmation bias when you try to justify reading internet when you need a kick and don't have energy for anything else. The rare instances when you used something you've learned beforehand on the internet are not enough to justify treating reading internet any different than any other form of recreation.

When you are aware of that, you may try to steer away yourself, when you are too bored to work (and preferably bit earlier) to other forms of recreation. Keep a bit of polymer clay at your desk and sculpt something when you are bored. Have a piece of paper and pencil and draw something (preferably some real object that's in your view than something from your head). Keep some legos and stick them together in random but perhaps weirdly symmetric fashion (don't over-think it). Play few levels of visually nice action game. Or just take a piece of paper and tear it bit by bit into pile of tiny bits. You'll be amazed of what's entertaining for your brain. Get up, walk around, go get yourself coffee or whatever, stare through a window at trees and people. Or just take a quick walk around your company building without any real purpose. Play a bit with some puzzles. Answer some questions on stackoverflow. Touch interesting 3d object with some textures. Jump few times. Basically do anything that's not intellectually taxing but exposes you to various stimuli you were lacking. Obviously try the things that are acceptable at your company. If you see group of friends talking about something interesting join in to listen (but make sure that it actually is interesting).

You can trick your brain into feeling that what you do is not that boring by listening to the music as you do it. But use this trick like coffee, sparsely, only when you need to focus but you can't take entertainment break.

On weekends and evenings you can still go on binges of reading, gaming, exercising, watching TV, sleeping, socializing, creating whatever keeps your brain non-bored.

One last thing, when you use sculpting or drawing as an entertainment please remember that you are not an artist. You are not doing it to create something, or like it, or be proud of it. You do it just to feed your senses for a while. Quality of your output is totally irrelevant. If you start thinking about your output you'll torch this activity as means of entertainment for yourself.