“Most promising signs yet” of alien life on a planet beyond our Solar System

Firstly that is completely badass science. The idea that you can use observations to detect the chemical composition of an exoplanet millions of kilometres away is an absolute triumph of the work of thousands of people over hundreds of years. Really amazing and deeply humbling to me.

Secondly, my prior was always that life existed outside of earth. It just seems so unlikely that we are somehow that special. If life developed here I always felt it overwhelmingly likely that it developed elsewhere too given how incredibly unfathomably vast the universe is.

If life is very common in the universe, then that is probably bad news for us. It means that civilizations should exist that are millions of years more technologically advanced than us; and should be leaving telltale signatures across the sky that we'd likely have detected by now. And the absence of those signs would be relatively strong evidence that life, while common, isn't long-lived. Suggesting that our demise too, will come before too long.

If, on the other hand, life is relatively rare, or we're the sole example, our future can't be statistically estimated that way.

Say another human-like civilisation existed and was more technologically advanced, what sort of tell-tale signs do you expect to see?

Scientists use the term "technosignatures", which you can google for more info. But broadly: radio signals, infrared from megastructures, optical signals like laser pulses. We haven't put a huge amount of effort in searching for such signatures, but there has been some.