As far as non-biased news sources go, your two best bets are going to be Reuters and AP News. Most of the news a vast majority of the population consumes, like CNN, Fox News, NY Times, you name it, are news outlets, not news sources.
Reuters and AP have thousands of journalists around the world reporting on breaking news the moment they happen and strive to deliver just the facts of the situations without bias, though of course any given topic could be considered biased depending on what your views are. Generally speaking, however, they do a pretty damn good job at keeping opinions out of their reporting.
The way CNN, Fox, etc., get most of their news is through paid newswires provided by Reuters and AP, sending the news directly to the outlets who then write their pieces on it, potentially adding additional information for context and any bias the news outlet may adhere to. CNN will often lean left, Fox News right, etc., and this will visibly reflect on their reporting because that is what their subscribers expect and want to read/hear while also being (for the most part) accurate.
The problem with your initial question in this context is that almost every news app I’ve ever used has been atrocious, both in UI and UX. I’m talking about news apps from the publications themselves, like the Reuters and AP official apps, not apps like Flipboard or Apple News, which I think mostly excel in the UI/UX department.
What I’ve tried in the past is using RSS for these, but the inherent problem is that there are so many news reports every day from these sources, and RSS does not typically have an option for sorting by something like “top news”. I think Feedly has something like that for popular RSS feeds, but then we hit problem #2 with this solution: neither AP nor Reuters offer RSS feeds anymore.
It’s a pain in the ass trying to get RSS feeds for both of them. They used to offer feeds, but now that everyone realizes that this circumvents the viewing of advertisements, they’ve essentially shuttered any way to grab just the text and images of news articles as they’re posted. I’ve tried every solution around, from FiveFilters’ Feed Creator to the many open source web scrapers available on Github, and the best I’ve found is a small site called PolitePol, to which I have no affiliation.
The results on PolitePol seem vastly superior to FiveFilters and others, and it was relatively painless to set up, though some feeds I tried required manually selecting CSS/HTML elements for the headlines and body text. Once you set them up though, they work great. Keep in mind that most of these RSS feed creation services will cost money, and PolitePol offers 20 feeds (without images) for free, but I chose the $10 plan for 50 feeds with images and a faster refresh rate. Not trying to advocate for any one service, this has just been my experience.
Yet after all of this, we still have the problem of RSS not sorting by Top News. I get very overwhelmed seeing hundreds of unread articles in my RSS reader, and quickly going through headlines is a slog sometimes, but it does work if you want it to.
The real problem lies with how awful these official news source/outlet apps are. I would gladly resubscribe to Apple News+ if it meant no giant ads between articles even for paying subscribers, but that’s unfortunately not an option at this time. The UI is fantastic, but these gigantic ads ruin the experience entirely in my opinion.
So, for me personally, I do a mix of RSS, occasional visits to Apple News, and visiting the news source’s direct website every so often to see the bigger picture. I apologize for such an incredibly long reply to this for a pretty basic point about biases lol, but hey, might as well post this since I typed it all out already.
I’ve told my staff not to mention sports scores in baseball, NFL, or college football to me anytime during their seasons.