Sure, those are other definitions [1], e.g. to prosecute an argument. Within a legal context, however, it is black and white.
> in the UK where you can bring a literal private prosecution
For crimes. One wouldn't say one is prosecuting a defendant for e.g. libel. (Some states have private prosecution [2].)
[1] https://www.merriam-webster.com/dictionary/prosecute
[2] https://en.wikipedia.org/wiki/Private_prosecution#United_Sta...
This is consistent with my understanding of the term as a native English speaker, having experienced the term "prosecute" being used in reference to both criminal and civil cases in all forms of discourse, verbal and written, formal and informal, for decades, and only first encountering the claim that it shouldn't be used for civil cases here in this thread, today.
Partly why I used that citation. It’s one of the few (adult) dictionaries that acknowledges as much.
I wouldn’t go so far as to say the Webster 3b usage is incorrect—it’s in some dictionaries and was historically unambiguously correct. But it’s non-standard to a high degree, to the extent that Black’s Law Dictionary only contains the criminal variant. (I’ll leave it open whether publicly referring to someone who has only been sued as someone who has been prosecuted, when intended as an attack, qualifies as defamation.)
More to the point of clear communication, I’d put it in a similar category as claiming one’s usage of terrific or silly was intended in its historic sense [1]. (Though I’ll admit my use of “nice” falls in that category.)
All that said, I’m very willing to entertain there being a dialect, probably in America, where the historic use is still common.
[1] https://www.mentalfloss.com/article/84307/7-words-mean-oppos...
The fact that you're referring to an intra-disciplinary dictionary to make the opposite argument implies that the narrower definition is jargon, and not an accurate representation of the common meaning of the term.