Begging the question isn't usually used like this these days, even if it did originate thus. The English language is used the way English speakers use it; yes, even that is quite circular, because there is no formal academy setting down rules that everyone agrees on. Institutions only teach stylistic choices. We use beg the question in exactly the way you say we shouldn't far more often than not to the point that its history is merely a bit of trivia, at least to most American English speakers; Oxford has yet to catch up, but I can't imagine the English situation is that much different than the American one.

https://www.grammarphobia.com/blog/2021/11/beg-the-question....