A sort of shower thought I had today about the order. If the order has existed for the better part of 500 years now and most apprentices are taken as children (so still in their formative years) is there a distinct hermetic culture?
At the very least you have covenborn and redcaps, plus all the apprentices who essentially grew up in covenants. Are there cultural mores and habits that those people have that would be noticeably different from people outside the order?
Arguably the order is much more egalitarian than is the norm in Europe at the time. Male and Female magi are treated as equals and democracy (to one degree or another) is fairly ingrained. Religious freedom is more of a thing too - not all magi are accepting of other faiths, but pagans, Christians, Muslims, Jews and more do all coexist relatively peacefully in the order.
You could also argue that the code is in a way a set of cultural values. Yes, it is a legal code, but that law is made and interpreted fairly democratically and a lot of magi are essentially raised from childhood with it as a code of acceptable conduct. Arguably the way magi think about scrying, or deprivation of magical power, or Certamen and Wizard War, are as much shared cultural values as they are codified law.
But what about other values? and what about other cultural aspects - fashion, music, literature, cuisine? Is there such a thing as "Hermetic cuisine" or "Hermetic theatre" or the like?