I get it, it’s the 32nd century and the glasses are maybe heads up displays that only he can see and use. But don’t you think in three thousand years they would have figured out how to build that stuff INTO or ONTO the eye? Instead of making the person, or the person choosing to wear an ancient form of corrective lenses.
His glasses are only the tip of the iceberg.
You bring up “showing up in medieval dress clothes” but that’s literally what Kovich is doing. In a room full of people in futuristic Starfleet uniforms, Kovich is wearing a vaguely futuristic suit and tie that is barely different from the fashion of the 21st century, and throwing holograms at Georgiou that have the exact same defects that 23rd century holograms did.
Kovich clearly has a thing for relics. It could tie into his interest in Georgiou as well.