I can understand Kate's feelings and ill-will about being upstaged by a young sexy newcomer. That's normal.
But that's when professionalism comes into play, in any line of work.
I could understand if, for example, Garrett acted up in such a poor fashion. But Kate is the experienced veteran performer, the "leader" of the cast and show. I'd expect her to set a better example and behave more professionally.
Plus, so many scenes and eps with Seven were directly about her interactions with Janeway. More scenes for Jeri usually meant more scenes for Kate, so what's the big deal?