Sure, there's a lot of evidence that they were "terra nullius" before being claimed for the British empire. But the Chagos archipelago was inhabited utill its population was compulsorily expelled in the mid twentieth century.

I was surprised to discover that Ascension even has a ccTLD. I guess I assumed that the population was wholly military.

That's because it was created by the same guy who created .io and .sh - British DNS "pioneer" Paul Kane, who clearly had a passion for finding remaining corners of the British Empire that could "claim" a bit of internet land (for his own profit).