Woah. Thank you for taking the time to read what I wrote. I hoped but hadn't expected that.

The thing about it which actually infuriates me, is that I think a lot of scientists actually kind of delight in this.

Have you ever heard the dictum "never ascribe to malice that which is adequately explained by incompetence"? A lot of experts really, really suck at explaining things, because explaining well is really, really hard.

It doesn't help that articles like the OP are aimed towards a mainstream audience assumed to have the attention span of a 5-year-old with ADD. The result is quick-and-dirty explanations that make the explainer feel like they explained something, and the reader feel like they learned something, but communication didn't actually happen. (My explanation was almost the length of the article. In order to cut it down to fit inside that article, it would have ended up equally as fruitful an explanation and drawn just as much ire as you.)

Aside:

Of course, a large reason for this whole problem is that the nature of scientific truths about reality has not yet been established among scientists (or really anyone in general, modulo a small group of philosophers I happen to agree with). So there is a sense in which it is "not their fault."

I think it's "not their fault" for the reasons I laid out in my previous two paragraphs. Every single elementary science student I have ever spoken to has put in some thought into the "nature of scientific truths about reality", enough that we feel like it's quite established among ourselves. I suspect you have a very specific, narrow notion of "[establishing] the nature of scientific truths about reality" that isn't what I have in mind, and that isn't relevant to why physics articles written for the layman have terrible explanations, either.

No, I do not think that is an acceptable description, because a surface is, by definition, defined as a 2D space within a 3D volume. You can't just throw out the definition.

Then what is an acceptable description?

What are you getting a PhD in? In every single academic field, people can and do extend definitions of terms that occur in plain English, because they study things laymen don't think about ("laymen" being our linguistic ideal of a "plain English speaker"), which is what the other commenter was trying to say about "plain English" being incapable of expressing abstract concepts in physics. Many academic fields also use technical terminology, but using jargon for every single thing that doesn't mean exactly what it means in plain English would require using a whole new language, I don't think that's what you're trying to say. But I don't understand what you are trying to say.

It's important to maintain the integrity of our concepts (including our definitions).

Have you heard of the "map-territory relation"? I agree that maintaining the integrity of our concepts is very important, and I agree that maintaining the integrity of our definitions is very important, but they're maintained in very different ways because they're not the same thing. Specifically, concepts themselves can't be allowed to be like one thing now and be like another thing later. We have to be able to state truths about a concept that are true in a way that can't change. Definitions, however, can change as long as they remain internally consistent and backwards-compatible with all previous important statements using such the definitions. This is done in every academic field, as explained in my previous paragraph.

Now that you have explained the whole reason for describing it that way to me, I understand what it is - but I could not have understood it before that, and neither could the vast majority of readers of that article.

I'm glad I was able to make you understand vaguely how 3D spaces could be curved. And I did just assert above that the article's explanation sucked. Now I'm going to argue that even so, it was fine: what did I explain, actually? I didn't actually explain in any more detail or clarity than the article how the universe might be curved? No, I explained what physicists and mathematicians mean when they talk about 3D space being curved (that distance doesn't bear the usual relationship to coordinates). Your understanding of the article is the same: it's been suggested that the universe might be curved, by analogy with how 2D surfaces can be curved, physicists measured some stuff, found that the universe is as close to flat as we can measure.

When you first read the article, you got super hung up on the problem that the universe isn't 2D, so why are they talking describing curvature of the universe in terms of curvature of 2D surfaces? And maybe this is an oversight by the authors, and they should've clarified that they were making analogy between curvature of 3D and 2D spaces. Or maybe most people who read the article don't get super hung up on this. The point stands that at worst it's a minor oversight.

To clarify my reason for defining a "surface" as I did. First, I think that's the actual everyday definition. More fundamentally - that is the only concrete thing in reality that people actually encounter. In other words, we do not encounter "3D surfaces" in reality, because that would require four dimensions. That fact is precisely why "surface" means what it does in English, and not what it (apparently) means in Physics.

"First...More fundamentally..." These do not appear to be distinct points. Am I misreading to interpret these as the same point: the "plain English" definition of surfaces is that they're 2D? That doesn't require clarification.

Although, re: "the only concrete thing in reality that people actually encounter...we do not encounter '3D surfaces' in reality", I'd agree with you more if you said "real life" rather than "reality".