@Sandro ******
and rather than make your own new post you resurrected a THIRTY TWO week old one 😮
I suspect you're not still on the original 90 days you get from the ED visa and if you looked at your stamp it probably says "extension of stay permitted until" 😉
Be that as it may, to go from an ED extension to a Non-B inside the country is totally between you, the school, your new employer and the immigration office.
You would take documentation from the school saying you are stopping studying on xxx date, go to the immigration office cancel your current ed extension, apply immediately for a 60 day covid extension and then apply for an in country 90 day Non-B visa IF your new employer can meet the documentation requirements for getting it issued.
GO with someone from your new employer to your immigration office and see if they will let you go from the ED extension to an in country Non-B. If they say no, your only option is to leave and get it in another country then come back.