In Portuguese, it’s used for nasalized vowels: ã õ. In the International Phonetic Alphabet too, it means vowel nasalization: ã ẽ ĩ õ ũ ỹ ə̃.
It started life as a little N written above another letter by medieval scribes trying to save space on expensive parchment.
The Wiki article you cite doesn’t mention the AP stylebook. Informality may or may not be the reason it isn’t used. Not that it matters. Its lack of use in this context means that it is not seen by readers. Why it isn’t used is less important to the question of whether people would recognize it than its replacement by the words about or approximately.
Interestingly, one of its approved uses hasn’t been mentioned yet. Apparently the Chicago Manual of Style requires a tilde as a line break indicator inside a long URL. Yet another usage that wouldn’t make “about” recognized as its meaning.
It can be used for equivalence relations. x ~ y would mean that x and y are in the same equivalence class. But there, it’s not a prefix/unary operator.
I don’t have access to the AP Stylebook to verify, but Google Gemini says there are explicit rules against using the tilde or plus sign as word replacements for ‘approximately’ and ‘and’.
There are exceptions to allow them for brand-names, LGBTQ+, and others.
I was half wrong. Tilde is not explicitly forbidden as approximately (in the 56th edition). There are rules in the Accent Marks section for usage in names and foreign language, but not a tilde in the Punctuation section. I think the absence makes it implicitly forbidden, but not positive.
In Japanese, it’s called a “wave dash” and has several meanings.
The main one from “from” such as “16:00 ~ 18:00”, from 4 PM to 6 PM.
It’s also used to elongate a vowel, which can soften a word.
Someone who assists elderly or disabled people with personal care and chores at home
I always took it to mean “approximately.”
But, there’s an electronic billboard near me that has had a series of messages such as:
“Live is Short. Eternity isn’t. ~ God.”
I’m not quite sure how to interpret that!
One use I’ve not seen mentioned is asymptotically equal f(x) ~ g(x) means the limit of f(x)/g(x) =1. x would typically be approaching 0 or infinity known by context.
I know this one, 'cause I do that! In that case it’s just a fancy “-”.
Either that, or it’s a message from Galactus, who is approximately God.