While this is impressive, it is neither the same algorithm, nor even the same type of language (I already know Julia is much slower than C). I don’t think it is much of a relevant comparison for a benchmark when almost nothing is the same except for the expected answer. Perhaps if Gauss Legendre were implemented in Mathematica it would only take 3 seconds! There’s no way for us to know.

does Mathematica actually compute it or is it just loading the value that it already knows?

Definitely computing. For arbitrary precision evaluation like this, Mathematica has always had cutting-edge algorithms built in.

As a random example: large matrix operations have been multi-threaded for ages.

7.6 second seems too much to be just loading a value from disk

it's not using the same algorithm right?