Breathable air would most likely indicate life on that planet which would lead a bunch of headlines. Our atmospheric oxygen is formed from biological processes and on most planets free oxygen disappears quickly. Short and medium term every scientific instrument capable of getting data from that system and any others like it would be pointed in that direction and we would end up with some new missions being funded to further confirm the data. I would expect a lot of geologists giving interviews saying "we don't know for sure but we don't think it's geological in origin, but maybe".

Beyond that, it would come down to what else is found. It's a REALLY interesting finding for about a thousand different reasons, but potentially confirming life on other planets is at the top of that list. I'd expect people to ask for a probe to go out there, only to be disappointed by the few hundred years of proposed travel time.