entombed in the shrine of zeroes and ones

Like any low-fidelity communication channel, languages benefit from error-correcting features. I think the feelings you're asking about are part of the selection pressure that explains why every language is full of weird little rules with weird little exceptions that are so easy to mess up. Think not about the mistakes, but what you feel when you hear someone say a sentence and you understand every word of it. Where does that confidence come from? Imagine someone describing the way to someone's house, aloud. And at the end, nobody's wondering "wait, did he mean turn AT the light or AFTER the light?" That's a tall order, even among native speakers. It's a little harder to imagine among speakers of different languages, but I've had ESL coworkers that I struggled to communicate with at first, but eventually we can discuss complicated technical topics with relative ease, and I can't really tell if it's because their English has massively improved, or if I've just learned to tune into the specific way they speak it.

I used to ponder the philosophical nature of how my language mistakes "feel" to native speakers of other languages, like when you wonder what your dog or cat smells on you, or whether everyone who sees blue sees the same blue. These days I just think of them as error-correcting protocols, like the Luhn checks on credit cards, or the checksums on TCP packets, and that makes it a little easier. There's got to be less geeky examples in the real world. But the reasoning is simple: You're sending information, but you include a little extra information, that means almost nothing on its own but increases the confidence that the rest of the information is OK.

The last digit of modern credit cards is based on all the previous digits, run through the Luhn algorithm. It's very simple, you can do it by hand, and any home computer can do it. So when you typed a credit card number into a website, it can tell if you made a typo before you even submit the form. Usually, your computer runs the Luhn algorithm on all but the last digit, and then compares its answer to the last digit. If they don't match, then at least one digit is wrong, but you don't know which, so you have to ask again.

Taking a common misgendering error in first-year Spanish: "Mano" is feminine in Spanish so "the hands" is "las manos". But it looks like a masculine noun, so someone might say "los manos" by mistake. If someone wants to say "I washed my hands" and says "Me lavé los manos" instead of "Me lavé las manos", then I can't speak for a listener's emotional response, but they'll probably notice the mistake, but they'll understand it perfectly. Later, that same speaker might refer to their hands by direct object pronoun, which in Spanish is the same as the definite article, and goes right before the predicate. So they'd say "Me los lavé" instead of "Me las lavé" for "I washed them." That's a grammatically correct sentence but strongly implies they're not talking about hands. Maybe they're talking about their fingers ("los dedos"). But a listener might remember the gaffe from earlier, and would be justified in asking the speaker what they washed. That's a data integrity problem. The speaker might resent having to repeat himself, until another guy comes in and says "¡lavé mis manos!" That sentence sure does sidestep the grammatical gender, maybe it's in some actual dialects in the US, but in the Mexican dialect of Spanish that my high school textbook was based, I can only assume that people would uniformly respond to a sentence like that by taking out a red pen and writing "-5" on you.

And I also realized that I've done this kind of thing in my native language, with other native speakers. Rooms and phone connections are noisy. People mumble. Regional accents exist. So when I suspect I'm not getting the message, I ask for clarification. And over time, I increasingly extend this courtesy to people who speak English as a second language whether it's rude or not. Nodding non-commitally and walking away is something you do to people you can ignore.

English-speakers, native and otherwise, will straight up leave words like "not" or "don't" out of sentences so often that I've developed a sixth sense for when it's happening. It's very visceral and I can't really describe the feeling, but I instinctively repeat their sentence back to them while it's still fresh in sense memory, and suddenly they'll interrupt "DIDN'T kill his wife" and we'll nod and laugh about how we almost slandered an innocent man but at least as proper white-collar Anglophones we use double-negatives. We DON'T use double-negatives. I think the reason every other language with double-negatives has kept them is because it corrects errors like that with redundancy.

There are a lot of people who have studied both linguistics and computer science more than me, and some cursory Googling suggests that "grammatical error correction" is a thing. And it makes a lot more sense than whenever I'm listening to a John McWhorter lecture or book, and once in a blue moon he says this about a language: "and this language requires you to include this word that doesn't mean anything, but if you leave it out, then they'll think you're a bit screwy." and he usually describes it as a social penalty, that a foreigner will lose points for making such a gaffe. Maybe it's because the source material doesn't include a description of the error-correcting that might ensue if someone gets the rule wrong, like "it raises doubt that you're talking about the same topic" or "it implies that you don't know what the word after it means" or even "it breaks the cadence of the sentence, so the listener lost their place and got a bit disoriented".