I don't think it could be confirmed by atmosphere alone, no telling how an atmosphere is composed on an alien planet. Detecting something like CFCs would be a really strong sign but still not 100% if there is some wacky geological process or unknown reactions from alien elements.

Edit: that being said focusing on a planet with CFCs in atmosphere would still be really cool anyway

I don't think breathable air counts as signs of industry. Although looks like JWST has found a planet with carbon dioxide which is interesting.

So you are right I guess that it could possibly detect industrial emissions.

Interestingly enough the planet with CO2 found is 700 light years away which could hint at industrial life there (but still going to be pretty hard to be certain), but if they were looking at us then they would only see Earth's atmosphere 700 years ago which would have a lot less CO2 then now.

But anyway in terms of electrical emissions, radio waves or seeing constructions on surface (or even orbital) I think it's pretty hard to get anything from the nearest solar system to ours, you can't just take a quick photo so everything is going to be super blurry

Even within the mily way there could be life, there could be life in Proxima Centauri, there could be life in Jovian moons.

Our detection isn't great, I think if we had an Earth clone in Proxima Centauri it would be hard to detect it has industrial life on it with any real certainty.