Disclaimer, I'm gonna info dump:
Most of the Grand Duchies and Archduchies are given because of them being related towards the royal and imperial family and/or they did something honorable/worth of merit, and sometimes, they're even regarded as someone on the same status as the royal and imperial family themselves with the perks of the same status, hence they even retain getting addressed to as "Your Highness" and such...
Hence though Alexis might be a Grand Duke and must be addressed as "Your Grace" like the other european monarchies, I think "Your Highness" is still fitting.
Plus in other european monarchy, the ruling houses are grand duchies and archduchies and uses "Your Majesty" and "Your Highness" to address monarchs and their children, so maybe the author made a reference towards those?
Actually, those referred to as "Your Highness" that are grand dukes or duchesses are only those related to the royal family. While this can vary from country to country, in general terms, when dealing with natural hierarchies in fictional or fantastical settings, grand dukes are referred to as "Your Grace". As our ML is not related to the the royal family by blood or marriage and was gifted his title, it is wholly inappropriate for him to be called "Your Highness", as this is meant to show distinction between those who carry royal blood and those who do not.
As a Duke, even a Grand Duke, he should be referred to as "Your Grace", not "Your Highness". It has bothered me this whole time. Lol.
Cute story. Funny, light and interesting.