The going-away party makes no sense, yeah. Actually I can believe that sometime in between Star burning down the village and her being sent to Earth, her parents were like "yeah you have to leave" and threw her a party to send her off and Star went along with it expecting it to be an empty threat and them to change their minds (I think the scene just transitions to her parents saying she can't handle it to Star begging not to be sent her away as her stuff's carried out, so its not like she was told she was getting booted off onscreen and there were presumably a few scenes we missed).
But she was told she was going to Earth like one literal minute before she went there, and we saw her enter the portal to it in the same scene. I mean I GUESS they could've spoken to the Diazes first, gone back to Mewni and had the party then, and then taken her back to school as we saw in the episode, since Star's wearing different outfits between leaving Mewni and arriving at the school. But that's an insane amount of contrivance just for that and was clearly not what anyone had in mind at the time the episode was made.
Star believing she was going to St. O's actually does make sense with the episode we have though, since she was only told she wasn't going there right before going to Earth. Even ignoring the going-away party stuff, it does seem like some time passed in-universe between her getting the wand and then getting sent to Earth, so she could have stressed about that offscreen.