...Indeed, the use of "probe" for crewed missions would probably be preferable in TOS "Tomorrow is Yesterday", where Captain Christopher's descendant is credited with leading the first "probe" to Saturn. It's much more glorious if he commands a crewed mission there than if he coordinates an unmanned flight (which by all rights should have taken place much, much earlier in the Trek timeline, and indeed would already have been in planning when the episode was filmed).
Of course, "probe" may also mean an investigation of non-exploration sort. The young Christopher might have been leading a legal inquiry into a badly botched first flight to Saturn, but again it would be less glorious than him commanding a crewed rocket flight there.
It's not impossible, though, that UESPA would have begun as an organization for managing uncrewed probe missions for the early United Earth in the 2060s or so, and would have retained the inaccurate historical name through the years.