Personally, I fixed the problem by not bothering with "staying informed" at all. I ditched media outside of local news entirely, and just don't engage with things that I can't do anything about. It would boil down to "focus on things you can control." Sure, it's fun to be outraged together with your friends about "X leader in Y country does Z crazy thing" but.. can you do anything about it? Does your opinion matter? Is there value in engaging with it? Turns out the answer is almost always no (unless you're suffering from main-character-syndrome, of course), so what's the point?
Focus on you. What are you doing today? What do you need to reflect on from yesterday? What do you need to plan for tomorrow? Don't waste cycles on things that are out of your scope.