International Remotely Sensed Aliens Day: How Will We Cope?

It probably depends on what we find. If we're talking about alien microbes or plant life, my guess is that there would be a lot of excited chatter and memeing, and that people would acclimate to it fairly quickly (though with a fringe of denialists as well). I mean, if I'm not mistaken, it hasn't even been a hundred years since we confirmed that there were other galaxies outside of ours, which is a mind-boggling discovery when you actually think about it, but I don't get the sense that it really impinged on people's everyday consciousness. I could see it sharply accelerating further space exploration.

If it happens that way, we would know that intelligent life existed millions of years ago

Not necessarily.
Sure, plenty of stars are that far away, but the nearest ones are less than 10 light years (there are actually 10 of these). Plus it may be how we find out there is life on Enceladus or Europa within our own Solar System.

i think o nate and jmm otm, i am actually much more interested in how we ppl cope when the 12 ft lizard cabal / hollow earth civilization / ai singularity finally reveals itself to us

As jmm pointed out, the effects probably depend on the nature of the discovery. A fungus on Enceladus is probably going to provoke an "Oh, cool" from most people. The sight of an approaching alien armada is likely to provoke either unheard-of unity, complete breakdown and chaos, or both.

to provoke either unheard-of unity, complete breakdown and chaos, or both.

This will depend on President Bill Pullman's availability

pretty convincing case from some scientists who worked on the viking probe that it could have found microbes on venus

https://www.scientificamerican.com/article/looking-for-life-on-mars-viking-experiment-team-member-reflects-on-divisive-findings/

we can talk to the in realtime if we have a wormhole phone

On Venus? That would be surprising--it's an environment very hostile to life as we know it.

oh wait, mars. sorry

we should just assume there is life everywhere beucase that makes more sense than "earth is the only planet with life because it is is special" - so lets just assume the alieans exist and hate us - and send giant tictacs to study us