Curious, any reason why the & isn't before the "R" like &Regular expression?

Yup! I had it there, but then it meant I you had to press alt+SHIFT+r to activate it! Because naturally it's a capital R. Seriously.

That doesn't make sense, we always use capital letters with accelerators (in brackets) in CJK localization. Like "正则表达式 (&R)", and we never have to press shift to use those. 👀

Yeah, that was surprising to me as well. I tried it, it did not work, so I moved to the nearest lowercase r. I may have had my focus in the wrong field when I did try it, but ... either way, it's one of the r keys now. 🙂

The method description could use a minor update. I'd particularly like an added description for what it means for this function to return false. Is it only if the provided regex was invalid?

maybe? Just something a bit more specific would be nice imo, because search->IsOk() is kinda ambiguous out-of-context.

Negative statuses denote warnings or infos. You should use status > U_ZERO_ERROR here.

nit: Instead of using results as an out parameter you could consider returnining a std::optional<std::vector<...>>, similar in spirit to a std::expected in the future (C++23).
It could then be split up here via something like

auto results = textBuffer.SearchText(needle, _flags, _results);
_ok = results.has_value();
_results = std::move(results).value_or({}); // std::optional has a && (move) overload

This would also potentially work well in other places like so:

const auto results = textBuffer.SearchText(needle, _flags, _results).value_or({});