It is pretty obvious if you search for any old topic that is also covered incessantly by the news. "royal family" is a good example. There's no way those news stories published an hour ago are listed first due to a high PageRank score (which necessarily depends on time to accumulate inbound links).

It depends on the content. The flip side is looking up a programming-related question and getting results from 2012.

I think they take different things into account based on the thing being searched.

Even your example would depend upon the context. There are many cases where a programming question in 2021 is identical to one from 2012, along with the answer. In those instances, would you rather a shallow answer from 2021 or an indepth answer from 2012? This is not meant to imply that older answers offer greater depth, yet a heavy bias towards recent material can produce that outcome in some circumstances.

If you're using tools/languages that change rapidly (like Kotlin, in my case), syntax from a few years ago will often be outdated.

Yes, yet there are programming questions that go beyond "how do I do X in language Y" or "how do I do X with library Y". The language and library specific questions are the ones where I would be less inclined to want additional depth anyhow, well, provided they aren't dependent upon some language or library specific implementation detail.

There are of course a variety of factors, including the popularity of the site the page is published on. The signals related to the site are often as important as the content on the page itself. Even different parts of the same site can lend varying weight to something published in that section.

Engagement, as measured in clicks and time spent on page, plays a big part.

But you're right, to a degree, as frequently updated pages can rank higher in many areas. A newly published page has been recently updated.

A lot depends on the (algorithmically perceived) topic too. Where news is concerned, you're completely right, algos are always going to favor newer content unless your search terms specify otherwise.

PageRank, in it's original form, is long dead. Inbound link related signals are much more complex and contextual now, and other types of signals get more weight.

Your Google search results show the date on articles do they not? If people are more likely to click on "Celebrity Net Worth (2021)" than "Celebrity Net Worth (2012)", then the algo will update to favour those results, because people are clicking on them.

The only definitive source on this would be the gatekeeper itself. But Google never says anything explicitly, because they don't want people gaming search rankings. Even though it happens anyway.