I tend to try to think of time as I think of space. If I clutter my space with a bunch of small things, I find that I think myself to be cluttered, and the disorder causes me unease. But if all the small things have their own places, and I keep putting them back when I take them out, it feels orderly, and there is no unease. It's really the same for me with time. If I clutter my time with a bunch of small, meaningless tasks (check facebook, check email, read that article that takes maybe 2 minutes, ..., loop), I find that that, too, causes me unease. But if I set aside time for those things, and only those things, there is no problem. I build things into a routine, as much as possible, and for the rest, I try to schedule the time I think I'll need, so that I can say "I don't need to think about X right now, because I will have time for it later."
I even try to schedule in periods where I do allow myself shallow work, like checking a bunch of things, or sating the information addiction that you and I most certainly share. Right now, I have maybe 50 tabs open between a bunch of aggregated tech/science news sites, and I'll spend maybe 1 minute at most on each one. If I did that just any time of day that I had a period of empty time, it would be just like if I left clutter anywhere that I had empty space. But since I've devoted this time to this task, it's kind of like putting everything you need for a project out on a table, then packing it up neatly when you're done with the project for the day. I know an end to the clutter is in sight, so it doesn't bother me so much.
The hardest part is always trying not to fill empty time meaninglessly. That takes skill, but it can be learned. I find I'm better at it when I've been keeping up with daily meditation in the morning and evening. But even if meditation isn't your thing, you can practice in other ways. For instance, when you are eating dinner, try to only be eating dinner. It seems awkward at first, to sit in silence (especially with a partner present) and just eat, but that fairly quickly goes away. Or, in the mornings, if you have coffee or tea, just drink coffee or tea and sit in silence. I tend to keep a notebook handy, and if something particularly strikes me during the silence, I write it down and let myself come back to it after I've finished my coffee.
I don't think it was any different before the popularity and ease of access of the internet. People assume that others were focusing on longer sessions of focus, but I don't think that's the entire truth. I think as a species, we've always struggled with this anxious itch to move on to the next thing, mere moments after starting the current thing. I think that's why (as you note) a lot of the older generations are turning to using the internet in much the same way as the younger generations.