Visa and permesso

I'm from Vietnam, I am currently a student in Perugia, Italy. I am studying Italian language. My student visa is type D and it is written " Studio, Corso di lingua" at the end, and my permesso di soggiorno is expired on 30/05/2020. My plan is after finish the language course, I study culinary in Italy
My question is: Do I have to go back to Vietnam to renew my visa? And if I have the enrollment letter of the culinary school, can I submit the documents to renew the visa in Italy?
Thank you for reading my topic and helping me.

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