I don't think there's a limit on how much you can process, but emotionally traumatic content like true crime documentaries can leave me pensive for a while.
There's too much happening for anyone to ever be completely informed, so we have to prioritize info we consume and make conclusions based on the limited information we allot time to gather. I think the busy-ness of modern life stresses the amount of free time we have and can commit to information. Hence the evolution of memes and headlines getting prioritized over substance. When people don't have time to investigate everything, they have to put trust in someone to make their conclusions for them.
It seems a little broad to suggest that all news is propaganda or poison. There's a LOT of counter mainstream news these days, which can still get caught up promoting propaganda, but you would never recognize it unless you consume a large variety of media with conflicting opinions. Not consuming any news is probably safer than consuming a limited amount, but if you have no life there's a higher perspective to be gleaned from investigating things from a neutral and open mind, and taking the time to research many sources. That's why I read every side of an issue I can find, to get as close to unbiased information as possible. There's apps these days that do what I do for people without the time; one is called Ground News. It collects all articles on a topic and rates their political bias, so you can see what all sides are saying.
I think that's where the threshold is. When you diminish bias and weigh multiple views, you find patterns that fit an underlying narrative, the real one. Without getting too political I feel like I've become radicalized over the past year by following that strategy of sifting through the chaos for clues of the truth. The truth I've seen is gloomy, even more than the mainstream gloom being cast around in the open. I guess that's a big motivation to read the news, people get a lot more interested when something big or scary happens. I have that interest chronically, like a bigger bad is happening on a longer scale than the 24hr cycle or election cycle.
Playing devil's advocate constantly, I think I have convinced myself of the dangers that drive my perceived need to stay critical of information that is passed around. Reading the news has become as much of a public service, pointing out events in the pattern to other people. Like "Hey, did you realize we're in water, and it's boiling? Look at the bubbles." I know that sounds biased, cuz a lot of people are radicalized these days through tailored news that amplifies their fears and conspiracies. Maybe I am paranoid and susceptible to certain doomsdays. Maybe it's biased to believe that more news consumption could equate to knowing more or knowing better.
Having a minority outlook just gets you outcast from mainstream groups, which pushes independents like myself to be even more critical of information being consumed. Promoting critical consumption of information is good for my political agenda

I think it's good to hear the info, judge it's authenticity, and try to understand why it's being told and believed.