It's hard to judge from the outside as you haven't shared the actual writing from UW.
I would probably cut this from the end of the LinkedIn post, this makes you look like you're possibly trying to blow this out of proportion for attention:
> I'm scheduled to graduate in a few months and am eager to move on to projects that don't need to be cleared with the UW Registrar. If you know of anyone looking for a full-time software engineer with a knack for getting the attention of senior leadership, please send them my way! I can start full-time in June
Your LinkedIn profile states you graduated high school mid 2023 and started at UW mid-late 2023. How can you graduate in a few months already? That would mean you'd just take 2 years instead of the normal 4?