The more I think about this the less sure I am that there will be an Imperial cultural norm either.
There would be a mythical norm (or stereotypical norm) that taken as an average of the nobility would exist, but no single noble would actually fit it exactly. It would be subject of endless glossy coffee table books by popular cultural commentators with names like "Holiday on Capital" or "The Third Imperium In Holographs" or something. When the heir-designate gets married dozens of wedding planners watch the videos avidly to capture the dress of the bride and groom and close copies (and dress inspired by it) pop up throughout the Imperium at weddings - the groom is seeing wearing a tailed coat! Suddenly every naval wedding features a jacket with a tailed coat and so on.
It would be based around noble (and very well-to-do) culture on Capital itself. Their customs and pageants would be endlessly recorded. Noble visitors and noble (and well-to-do) sons and daughters who are being educated on Capital would bring it back to their home regions. "Exiled" nobles would follow it (be they exiled by politics or on some multiyear "mission"), and anyone who wanted to "up with the latest fashions" would watch and follow it avidly. This would establish a rough "Imperial" culture in various regions.
From there, the lower and local nobility would follow the trends of the "high" local nobility. The wealthy-and-powerful-but-not-necessarily noble would copy the local nobility to give themselves an air of exclusivity. And of course, the middle class, ever wishing to appear more like the upper class and not the lower class would ape the wealthy as they always do.
At every level there would be dilution of "Imperial" culture to be replaced by local norms and sensibilities. Of course, Imperial culture would also be marked by its willingness to embrace local customs as well - like some Illeish duke well known for his good taste and his appeal to the ladies might influence the entire young male set of Capital nobles into wearing vaguely Illeish styles.
You could even introduce some humorous custom that got started like that. For instance, perhaps at some Imperial reception for frontier nobles the Emperor, when he had a moment alone, was seen to raise his tea service towards the noon sun. As it was the summer solstice, many of the frontier nobles, not wanting to embarrass themselves copied the Emperor's gesture. This was, of course all recorded. The stately way which he did this caught on and soon the Archdukes were seen doing it locally. Various commentators attributed various meanings to the custom. By the present day in the game, perhaps it's a staple custom.
However, to those truly in know, it wasn't really intended to be a custom. The Emperor had noticed a lot of spilled tea in his saucer, and in an alone moment, was holding his teacup up to see if there was a crack in it as he didn't think he had spilled that much. Of course, when everyone else copied him, eager not to offend, he didn't want to embarrass anyone by calling people on their mindless copying.