While an institution's reliability and bias can shift over time, I think AP and Reuters currently fit the bill. They report the facts the most reliably of any big-name general news sources I know of, without very much analysis or opinion. Their political leaning is nearly neutral or balanced, but maybe on the left side of the line (Reuters might be slightly less biased than AP, but still on the left side).
The Wall Street Journal is a little bit less reliable on the facts, also centrist, and on the right side of the line due to their business focus. If you read this too, it may help you counterbalance AP's and Reuters' slight left bias without going to the unreliable right-wing extremist sources.
If you want only one source, The Hill is about as nonpartisan as it gets (maybe a bit less reliable on the facts than the WSJ, but still pretty good). They report on both sides of the aisle. Their focus is, in their words, "on the inner workings of Congress and the nexus of politics and business".
[Epistemic status: I looked at the Ad Fontes Media Bias Chart. Exactly how impartial their judgements are, I can't say, but they do seem to try. Media Bias/Fact Check mostly agrees with these judgements, but I don't think they're any more reliable.]
That said, even an "impartial" news source (to the extent there is such a thing) is going to give you a very distorted view of the world due to selection biases and the Overton Window. "Newsworthy" stories are, by their nature, rare occurrences, and will tend to amplify your availability bias. Don't lose sight of base rates. Our World in Data should be worth exploring for that reason. They publish what they think is important rather than what is new.
I skim the headlines for several topics on news.google.com. I read the Wikipedia current events portal. Stat is good for more depth, but covers fewer topics.
+1 for Wikipedia, that's how I find out most of my info on current events. If there's something that seems likely to be important to my near-term decision-making (e.g. riots near me) I'm likely to Google for it to find more details, but Wikipedia is a good place to find out 'what are the major things that are happening in the world right now, in broad strokes'.
The Economist ($) for non-Western events and live macroeconomics. They generally foreground the most important thing that happens every week, wherever it happens to occur. They pack the gist into a two page summary, "The World this Week". Their slant is pro-market pro-democracy pro-welfare pro-rights, rarely gets in the way. The obituaries are often extremely moving.
AP, Reuters, Bloomberg, Pew Research, Bureau of Investigative Journalism.
FT and Economist have degraded somewhat but still good.
Pew Research is nonpartisan and has a reputation for factual accuracy. They're more of a think tank than a newspaper--not a news organization that would tell you the current events of the past three days (although they do a lot of polls about current events).
Bloomberg is rated "left-of-center bias" by Media Bias/Fact Check.
I agree with the rest of your answer though.
While the current events portal on Wikipedia has already been mentioned, I prefer the much more concise annual summary pages which I check monthly. The page gets updated quickly with any major events that happen in the world.
Naked Capitalism produces a very good daily roundup from (usually) reputable sources, well worth a skim through.
https://www.nakedcapitalism.com/
Project syndicate provides in-depth coverage of current events
https://www.project-syndicate.org/
https://indianpunchline.com/ and https://supchina.com/ provide counter-narrative views on events in their respective countries
The Financial Times, maybe FiveThirtyEight
hedonometer.org is a quick way to check if something big has happened
I like FiveThirtyEight, but it's not the sort of publication you can refer to for "what happened in the past 3 days" (except for very specific events like 'how much Trump's popularity changed in the intervening period').
I second the Financial Times recommendation.
Reuters is my "just the facts" RSS feed of choice - but I understand the Associated Press (AP) also plays a similar role as a newswire service reporting bare facts on the ground, which other outlets then often use as their source for longer articles that add context and analysis.
That said, I usually just skim through Reuters' headlines, as the article is often just the same basic atom of fact as the headline, elaborated out into more words.
The articles I read the full text of come from a spread of other outlets with different biases. Nothing off on the fringe that would fabricate stories - just mainstream outlets with enough of a reputation to uphold that I don't expect they'd try to outright lie.
I lack a good answer for you. I find all the suggested sources okay and read them myself in most cases (FT and Economists no but used to long ago).
I also read South Morning China Post and Al Jazeera (and some Korean papers) for non western perspectives. I keep saying I should add some of the continental European papers.
Occasionally I will check out something from Russia and some of the party mainland China papers as well as Japanese.
I look at a couple of Philippine papers as well for personal reasons and sometimes get a new insight to a larger theme.
I don't think any are unbiased and non really seem to try to be completely objective. That is why I would suggest reading several version of the same story. Basically, it's the application of the old saying, your side, my side and somewhere in between is the truth.
I've longed assumed that the vast majority of what the news discusses is irrelevant in the long run, and not that well reported at that. But the world seems to be moving faster these days, and I have more of a sense that I want to know what happened this week, because it might impact what I do next week.
For the first time in my life, I have some inclination to follow current events as they happen. And I find that I don't really know how to do that.
What are the most reliable / least-politicized news sources?
In particular, I want a resource that I can refer to that will tell me what happened in the past 3 days, in as factual and unbiased a way as possible. I expect that I might have to do further research, to get context for the events. But to start, I want a place where I can go that will tell me what happened, with a minimum of narrativizing, political outrage, etc.