He was assigned as part of her platoon after graduating from Cadet Corps. In Light Novel, due to admonishment of his status as volunteer by Tanya, he acted rebellious against her. He was re-assigned by Schwarzkopf togerther with Harald von Vist.
In anime, he was shown to be dissatisfied of Tanya's leadership and presumably have some bias against her due to her young age.
He was a classmate from the same wing due to their status as volunteer, so they were also a pair due to their familiarity. Not much shown about their relationshipin Light Novel and Manga.
Anime depicted their dynamic as a pair of like minded comrades, and Kurst appear to be the one who call the shot in their partnership. This could be seen from how Harald followed Kurst in his reckless charge against Tanya's order, and later on supporting his protest for their dismissal.
In Light Novel and Manga, they're not very familiar because they belong to different wing because of his volunteer status. Not much interaction shown in either media.
In anime they are classmates and have some degree of familiarity enough for Visha to be worried of their absence. While they weren't close, Kurst was civil enough to tell Visha that she had to eat to replenish herself even if she was tired.