It's crazy how often these simple rules are violated.

Sometimes someone will tell a story to be that involves 3+ people, and they'll slowly switch to using pronouns instead of names. I feel a bit like a jerk for continually interrupting them to clarify, but only when they're unfazed and happy to provide the clarification do I realize that this is just how their conversations usually go.

Yes. I often feel like I'm being too pedantic when asking for clarification about who is doing what from people since I do it way more often than others, and honestly can't tell if I'm just not thinking hard enough about it to intuit the likely correct answer or most people just let it go much longer and eventually work it out from context or assume and risk being wrong.

Pronouns are truly the bane of clear communication.

I set this rule for my team so many times and it's awesome how much harder people have to think, and how much better the team works when people can't write a sentence like "It's not working right do you know if anything changed with it?"

Me: "What's the problem"

Them: "You know, the thing with the thing"

Am I misunderstanding "one-word" here? So far as I can see there's nothing wrong with the pronoun use in these, all of which have more-than-one-word antecedents:

"The last-but-one president of the United States met today with his former press secretary."

"My favourite blues singer stubbed her toe."

"That wretched web browser I hate is updating itself again."

I don't know the grammar terminology (ESL, and all), but AIUI, in your examples, the one-word antecedent would be, in order, "president" and "singer".

What I do understand though is the wider point: ambiguous sentences are a pain for AI and humans alike; if you use a pronoun, make sure there is exactly one candidate it could refer to.

"one word antecedents" means that the pronoun can refer to a single word (and only one).

So in "The last-but-one president of the United States met today with his former press secretary." we see "his" refers to [the] "president".

A counter example would be:

"The last-but-one president of the United States and his partner met today with their former press secretary."

In this case "their" could refer to to the president, his partner or the collective of the president and his partner.

This seems like an odd use of language to me -- the pronoun refers back to a particular thing, not a particular word, and the thing that's needed for clarity and definiteness is that there should be one thing, not one word.

Consider:

"The puzzle contained one red herring; it led a few solvers to waste some time." (Antecedent is "red herring"; a red herring is not actually a herring and it doesn't make much sense to say that what the pronoun refers back to is "herring".)

"The puzzle contained three red herrings, of which the last but one was particularly liable to confuse; it caught out many solvers." (Antecedent is "the last but one [of the three red herrings]"; if you had to pick out a single word it would have to be either "herrings", which is plural, or "last", which is Just Plain Wrong.)

"Mary went through the list of candidates to find the most suitable for the job. She sent him an email containing a job offer." (Antecedent is "the most suitable for the job". No single word will do.)

I'm guessing that "one-word antecedent" is US educational jargon. I don't like it.

A couple of more drastic examples to ram home the point that pronouns refer to things (or maybe ideas of things) rather than to words as such.

You and I walk into the office and I point at one of the people sitting at a computer. "He's one of our best engineers. You should give him a pay rise." (The antecedent is merely gestured at, not mentioned in words at all.)

I come into the room where you're listening to Bach's "Well-Tempered Clavier", and say "He's so good at fugues." (The antecedent is merely implied by context. No words, no gestures, nothing.)