You just... stop caring. The only two good reasons to pay attention to news are if it affects you in some way, or if you can do anything about it. The vast majority of news is in neither group.
That's the first pass. From there, you adjust your definition of "affects you". I'm in the US, for example, and our government does plenty of bad things I do not approve of. But most of them, even the ones that ostensibly should affect me, don't actually noticeably change anything in my life. After a while, it all blurs into "my team scored a point" or "the other team scored a point".
Is this privileged? Of course. But it's also a requirement for my mental health. Paying attention to it wouldn't even improve anything for the people who are suffering, so there's not even any sort of utilitarian tradeoff. It would just be making my life worse for no reason, so I don't.