“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.

It is quite plausible that life is abundant, but sentience is not. If we take Earth, it formed 4.5 billions years ago, conditions became suitable to support life like 4B years ago and first known signs of life are dated 3.7B years ago.

Now, in just .5B years Earth would likely become uninhabitable due to Sun becoming a red giant. In other words, on Earth life spent 90% of its total available time before sentience emerged. So on one side life is constrained simply by time, and on the other, sentience might not be necessary for organisms to thrive: crocodiles are doing just fine without one for hundreds of millions of years. To think of it, it is only needed for those who can't adapt to the environment without it, so humans really might be very special, indeed.

The sun has about 5B years more to go before it turns into a red giant, not 0.5B years...

While it has more time to become a red giant, it'll become more luminous over time and life on Earth will be impossible much earlier. I've seen estimates of 0.5B to 1.5B years.