Well Aquilonian and Poitain knights wore plate which wasn’t really a thing until the 1400s.
“The Aquilonian host has assumed the customary formation; the strongest part was the center, composed entirely of heavily armed knights; the wings were made up of smaller bodies of horsemen, mounted men-at-arms, mostly, supported by pikemen and archers. The latter were Bossonians from the western marches, strongly built men of medium stature, in leathern jackets and iron head-pieces.” from The Hour of the Dragon pg. 99
Conan himself wears everything from a loincloth, silk breeches, to various types of full armor.
Yet a proper armscrye for clothing was not developed til well into the renaissance.
Then we’ve got the infamous chainmaille bikini and all the scanty “barbaric” clothing that was the staple of the Conan bookcover art of the 70s all the way up til present day.
The truth is the level of tech (and fashion!) is all over the place in the Conan genre. And Conan spent a fair amount of his own time “out piratin!” So I’m gonna cut them a break here and just enjoy the outfit because it’s really not all that far out for the genre.
Now if you want something to actually be annoyed by…