Moving back to Japan, didn’t submit moving out form or pay some bills because I didn’t know about them… what’s the likelihood this will affect my visa, and how do I fix the problem?

I was in Japan for 5 months as an intern from May to September of 2024.

I was paid a small, part-time wage of ~200,000 yen total during my time in Japan, by my internship (a university).

Unfortunately I did not pay health insurance, taxes, or pension. A previous intern who came back to work at the university told me I didn't have to pay any of that since I was only going to be in the country for 5 months. It turns out she meant don't have to pay as in "you won't get caught", not "you legally don't have to pay".

I legitimately thought I didn't need to pay any of these bills. I also had no idea about the "moving out" form I should have filed with the city hall, I simply never heard about this and left without doing it. (My internship was fairly unique and… disorganized, to say the least). I did get my residence card punched/visa cancelled when I left.

I now have a job offer to come back to Japan and work full time, including a new visa which will be sponsored by the company.

I have two main questions:

1) Do I have to worry about my unpaid pension/tax/healthcare affecting my visa being issued? Reading through reddit, I see many people saying that it doesn't matter and my visa should be accepted, but I may have to pay these bills when I get back. (I want to correct my mistakes so I am happy to pay. And I think the total bills should be less than 50k yen.) But I am a bit nervous and want to hear people's thoughts.

2) how do I fix this when I return? Can I simply go to my old city hall, explain my situation, and pay everything there?

Thank you for your help!