Notifying immigration about job searching

I worked as a haken from october to december on my working holiday visa and they sponsored me to change to a specialist in humanities visa, which I got aproved and got my new zairyu card in february.

The thing is I had been searching for jobs with them since january but I wasnt able to get any so last week I told them I would search by myself so they gave me the 退職証明書 where it says I worked with them until the end of december. Technically I was still on a working holiday visa in january so Ive only been unemployed since february but I didnt notify that I left my job cause I was still job hunting with my haken company so I dont know what should I do…

The girl from the Haken company told me I should notify to immigration that I am job hunting, but wouldnt I get in trouble since the 退職証明書 says I dont have a job since december? I actually separated from my haken last week but the paper does not say so so I am not sure what should I do.

Should I go to immigration and told them what happened or should just send a notification when I get my next job?

If anyone knows anything or can help me please thank you so much!!

by babababa5081