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?
This can happen, if people are raised in a "large, old covenant thst has little contact with the outside world". See ArM5 p.52 Covenant Upbringing. Also covenants that are less isolated may still impart specific values to those raised within.
I would expect, that covenant culture is more specific to a covenant, and varies greatly in the Order: certainly with respect to "fashion, music, literature, cuisine".
Taking a look at literature: The Travels of Fedoso and Erika's Story are books used for education only in covenants, and in many ones. But are they used in the Theban Tribunal as well - or is there already a language barrier?
Who reads Alcuin of York's Propositiones ad acuendos iuvenes? Who Aesop's Fables?
Common culture starts with a cultural memory, which for bookish magi will certainly require a common historiography (see e. g. Jan Assmann: Das kulturelle Gedächtnis). So is there a tradition of historiography of the Order of Hermes at Durenmar beyond just Xavier of Mercere (GotF p.61), which is respected all over the Order? Or is the library of Durenmar just a huge and underused archive of the Order's past? That could be a topic for an article in Sub Rosa.
Fashion and music: probably still dictated by the regions of origin and living
Literature: most definitely. Considering how few books people would normally have, aside from bibles, the Order's hermetic texts would probably follow a limited number of currents of thought and styles, with disagreements over the citation styles between the 2-3 main ways.
Theatre: probably something loosely based on the chanson de gestes, with a few Normandy/Provencal Covenants exporting troubadour/trobairitz across the order, who have their own subset of Hermetic Dramas, in latin, depicting famous hermetic adventures.
Cuisine: edible beasts of virtues would be prized as supreme specimens fit only for the finest Jerbiton gourmets, who'd pay outrageous sums for Flambeau hunters to bring them back Venison of Virtue for their next major feast. Given the ease with which food can be flavoured with spice of improved with magic and spice, the first covenants to have developed those spells probably set the trend "Sea food a la Florum" or the "Dunremar Maultaschen recipe" which everyone knows of since it is served at every Grand Tribunal.
Well. Old and large covenants are known to develop distinct cultures. Pidgin languages are explicit in canon, but I am sure music and cuisine developed by blending local customs with whatever strange things the magi can import, would be common.
Houses also have their own canon cultures. Verditius with their contests and bragging, Flambeau with their tournaments, and Bjornar with their mysteries. I am sure their events come with music and theatre and so on as well.
Now, is there room to develop a Hermetic culture which bridge these cultural differences and yet is distinct from the rest of the known world? I would be surprised. There are not that many magi, not even when you count covenfolk, and they do not meet that often.
Some other value that should be more prominent in magi than in mundanes is the respect to their elders, if only because mundane elders tend to be fragile, while hermetic elder might be quite powerful and not exactly fragile (or, if they are, know their ways around it well enough).
Magic spells to improve flavour might not be very popular. "And now if you are kind enough to lower your Parma so the improving taste spell can penetrate..."
You can also expect the exact opposite. The same as we as a technologically based society appreciate and valuate handmade products, so could do a magically based society. Any magus early on his career can get himself a Mystic Tower or get an omelette that tastes like ambrosia, so if you want to display power and might get that tower build over the sweat of the best mundane craftsmen of their time (or a handful of generations of them if you want to score real high) and serve your guests an omelette made by the best cook on Mythic Europe.
(So probably a custom of at least some old powerful magi will be to collect craftsmen).
Considering how easy the taste of spice and herbs spell is (level 5 MuIm), I would imagine that at some point a mage would have just made a high pen item of it, just because they liked Saffron heavy Gingerbread.
You mean House Verditius right? Because even barely past gauntlet, my Verditius player got himself a craft: iron lab assistant.
Interesting point. The only other mention of historical writing in the order I can think of (besides what you already mentioned) is the popularity of biographical works in the Hibernian tribunal, but it explicitly says there that the continental magi mostly view that as a distraction from studying the arts and inventing spells.
Which is a pity, because I think some hagiographic "Lives of the Archmagi" style books for the order are both a neat idea and a good vehicle for dropping plot hooks. Maybe my Hibernian is showing...
Even if there is no authoritative historical account that the order universally recognises, there must be an oral tradition of some kind. I would assume at the bare minimum most magi know the story of the founding of the order, plus some of their own house's history, just from exposure. Most magi have a score in Order of Hermes Lore and (Organisation) Lore abilities do cover history and legends, among other things.
edit: There's a second mention of historiography in TCI. The Red Book of Cloyne is a chronicle of the history of the Hibernian tribunal, and is apparently considered authoritative (helped by being compiled by redcaps who all study the art of memory) but has not been available to anyone but redcaps since the Schism war. There is a hook related to magi complaining about this lack of access.
Here's my thought "church culture" was certainly a thing for a large organization which had even less capacity to meet in person and communicate over long distances than the order.
In fact their probably should be a hermetic culture, the problem being that the system has already been set up with independent cultures for 12 houses and 13 tribunals, each independent of the other with frequently clashing intersections (Hibernia has its own naming conventions, as do Bjorner, so how do bjorner in Hibernia pick names?) It is a system that falls apart if you look at it too hard, and trying to add a capstone hermetic culture pretty much requires looking at it too hard.
Jan Assmann in Das kulturelle Gedächtnis explains, that oral memory fades after some 60 years, unless it is codified in writing ... or in texts like early epics learned by heart and recited ceremoniously, of which e. g. Ilias and Odyssey conserve something.
But if the bookish and intellectual magi don't have a valued, debated and maintained written historiography, they lack the fundament for a common culture.
Perhaps oral memory lasts longer when the average person lives to be 120 instead of the somewhere between 23 and 35 I would expect for the middle ages.
There is definitely some form of common mythology with mythologized but historical foundation story, that is shared among all magi.
Along with the code of hermes that is some evidence of a common hermetic culture.
I think also that the christian parts of the order of Hermes would have its own lively religious culture with different viewpoints on how christianity ought to be and what the role of magi and magic is in christianity.
Wouldn't work: the target of the effect is the food, not the magus, so penetration only helps if the food has magic resistance. The problem is that magically enhanced food is under an active effect, and there's no real way around lowering your parma for that (which also allows in any other effect on it).
(Magically-enhanced food is however great for treating the covenfolk).
The Tribunal books for 5th edition make a point of showing how different the local Hermetic culture and peripheral code is for everywhere except Provence, which is supposed to stick closely to the (loosely-sketched) "default".
I remember in Against The Dark that House Tremere keep records. Now looking at this book, page 24 mentions under "co-option" that "The House spreads its ideas through literature (which is why so
many of its servants are literate), and through theater and art (which is why it sponsors Redcaps who tour with plays)." In fact this whole section mentions a lot about Tremere culture.
The section on Tablinum mentions all the different exhibits it has (I love this hermetic museum) and page 63 it has a section on the "Transylvanian chronicle", so Tremere have an official record of what they say went on in this tribunal (although it is mysteriously quiet on the founding of house Tremere and the build-up to the Schism War.)
I like to think that between House Mercere records, Magvillus recording legal decisions and details of traitors to the order, Bonisagus sharing their research, and the vanity of wizards who want to write books but the only thing they are experts on is Organisation Lore: Order of Hermes from gossiping with other magi, that there are a decent number of written records. In fact, if they don't exist then we don't get to use the plotlines of "The Duresca Scrolls" or from Sub Rosa "The Gaer Hill letter".
Of course the history leaves bits out - why else are you discouraged from poking around Diedne ruins? Is it because they don't want you falling to their type of corruption, or because they don't want you disturbing ghosts, or is it because they don't want you uncovering inconvenient truths.
I played a saga for over three years set in York, where our covenant was Autocephalous because it's income source was St. Peter's School and they had a charter. We did not consult the work of Alcuin (our most famous headmaster) once in decades of saga time. His stuff was those dusty books in the back of the mundane library, whereas we had hired-in tutors from fine universities to do the actual teaching work.
-- and the settlers of the 16th and 17th century in North America had already brought with them millennia of European history!
EDIT: Still, an American friend told me many years ago, that 100 years are a long time for an American, and 100 miles a long way for a European. The Order of Hermes may be affected by both types of blinkers.
This fits nicely with the fragmented, partly secretized, historiography of the Order which these Tribunal books also describe, and the need to rediscover fruitful parts of the Order's history described in LoH.
So far we do not find a cohesive common Hermetic Culture in the Order beyond the Code and derived peripheral codes. The intention behind this might be, to not distract from Mythic Europe with an artificial Hermetic Culture. Such an artificial Hermetic Culture would also further raise the barrier to invent magi for gaming in Mythic Europe.
Magi from many different cultural backgrounds, derived from the histories and legends of the middle ages, coexist in the Order. This Order develops together with the scholarship and philosophy of the middle ages (see e. g. A&A p.11), depending there very much on learning and creativity of mundanes.