Once word gets out, the UFP would be defending the Baku against the Romulans,
Assuming the Romulans would want to risk violating the Neutral Zone and starting a war anyway. Depending on where that is in relation to the Baku planet
The Ferengi are going to bring military force on someone? Really? The most they would do would be to try to buy the Baku off.
Are either at war with the federation or rebuilding their smoking ruin of a homeworld with millions dead depending on the timeline, I doubt they would spare the resources of either seeing as in once case the Starfleet will already shoot them on sight and the other they need federation support just to keep their empire from collapsing.
Of course all this rests on whether or not ALIEN civilizations would care about a fountain of youth
,.... etc. You think if a "fountain of youth" were discovered on Earth there wouldn't be some competition for it?
Yes but on Earth we would have a better idea where the various borders would be in relation to said fountain as well as a more accurate assessment of the political landscape of the area seeing as how their Neutral zones that violation of are an act of war and interstellar wars and the rebuilding in the aftermath of such at that point in the Star Trek universe.