1. News networks would not cover it
2. Disinformation networks would kick in at high speed
3. Only the "crazies" would believe it
4. The "crazies" would lose their PayPal accounts

It would be an amazing discovery, but life will go on as normal. After all, you can’t be fully certain that it is like that because of life until you see it. Perhaps other signs besides breathable air will support it.

people that already want to believe in life would believe

people that are skeptical would remain skeptical

nothing would really change.

Short term excitement and then back to normal. There's not much we could really do about it other than acknowledge it's there.

I think it would create shock in the scientific community, and institutions that are created around the scientific community, but it wouldn't create culture shock.

If moss was found on some exoplanet for instance, the scientific community would be very excited. Meanwhile, most (I'm guessing here obviously) people wouldn't realize how big of a deal that is, or might wonder "why we spend so much money to find moss". That's not a judgement on anybody, but I do think a lot of people would fall into that category. I think it would be the same if we detected breathable air.

If you want culture shock, you'll have find and invite a little green man aboard the ISS and somehow convince people that it's authentic.

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.

Then we should send a probe there at 99% the speed of light.
Perhaps we'd hear back in a few generations.

Even if we detected 100% certain alien life, not much would change imo. Normies would just go "Huh, neat! Anyway, can you believe what Kayne said", and governments would just assess it as a threat and keep telescopes pointed that way to see what they could learn

Even when the UFO disclosure was going on over the last few years, with the Pentagon itself outright saying "There are unknown objects stalking out naval ships and flying past our military bases" nobody cared. If you even try to talk to people about it, it's just "Huh that's weird, probably the Chinese / Russians" as if that also isn't a very scary thing

IMO the US government could outright say "Aliens are living on Mars and we've contacted them" and people would still not really care and would just go on with their lives and go back to work etc.

We should send people there. I can think of a few.