You’re right, but that’s the ‘paradox’. Given our most pessimistic estimates for the chances of life we should have seen at least something that was a huge give away by now. Maybe better telescopes and observation methods will find them, we can get a spectrum from exoplanets. That’s incredible; but so far all we see with our telescopes is more lifeless space. That doesn’t mean they’re not out there, it means our estimates are wrong. It probably means that we just don’t understand what factors are required to create life very well and advanced life is incredibly rare.

And yet. We wouldn’t see ourselves from Alpha Centari unless there was deliberate directed transmission.