Since no one else has done it, I'll plug the Canadian Brass recording -- it's one of my favorite recordings of the Art of the Fugue, and (among many other things) just shows how flexible and instrument-agnostic this music is.
It’s not music from the classical period. Indeed, it’s from the baroque period. But in my decades of talking about and performing classical music, the term has never led to confusion.
That comment is mind boggling. I've spent a large fraction of my life playing in classical orchestras and also never heard anyone get confused. Yes, classical music is a genre and a period. Bach is in the genre, but not the period.
I hope the commenter learned something from their attempt at pedantry.
There are two uses of classical in modern parlance: classical as in the classical Mozart period, and classical as in anything that spans from Baroque to the late romantic Rachmaninov era and other composed music that uses largely traditional harmony or atonal music along the lines of Shoenberg.
I love this one too, and spent an incredible amount of time identifying the particular recording from audio memory as a kid in the 90s when my dad used to play it. Really excellent renditions, and I'm no classical music buff, it's just almost objectively brilliant regardless of musical tastes.
I adore the Canadian Brass' recording, and also the other Bach pieces they have transcribed.
I'd also like to plug the album released by the Academy of St. Martin in the Fields, who did a double album of the Art of Fugue and the Musical Offering, and used a variety of different scorings for each movement.