Student visa run to korea

My exchange is ending soon and I had some questions about leaving and re-entering.

Some background: My residence card expiry is July 2026 as my visa was for 1 year but my uni told me it's actually only valid for 7 months. I understand that my visa technically ends on the date that I finish studying so that was no problem.

I just finished up my uni semester and because I assumed that I could stay for 3 extra months according to article 22-4 (v) of immigration law, I booked my return flight for March 16th. But now my university has told me that I must leave within this month or I will be breaking the law as illegal overstay.

They said they told immigration that my leave date was 31st January (a date which they said they've changed multiple times (?) but I had no knowledge of this. It was probably related to the fact that I returned my student id on the 30th Jan but I'm not sure.

They told me that leaving on 27th of February is ok. But that will cost me 35,000 yen.

I wanted to change my status to temp visitor within Japan if possible but after looking at some other reddit threads I'm not sure if that's possible.

So I was wondering, what if I did a visa run and went to South Korea on the 27th for a week to travel, and then came back to Japan on a tourist visa until my flight on March 16th? Is that allowed? Will immigration deny my re-entry? I consulted ChatGPT (I'm sorry for the wasted water..) and they said it was too risky as it will seem suspicious since I just finished my long-term student visa stay, and it'll look bad for when I want to return to Japan for work/school again.

Thank you for the help!

by boopbadoopshwoop