Visa question

Good day,

I hold a Schengen tourist visa valid from November 2022 to November 2024 (multiple entry). Last year, in early November, I came to Barcelona to study at a language school. Due to some problems with embassies in my home country, I entered Barcelona on a tourist Schengen visa and applied for a student visa while already in Spain. My studies started at the end of November 2022, but I only received my Spanish student visa (D-type national visa) in April 2023, due to the high volume of applications. (This visa still covers my studies from November 2022 onwards). This student visa will expire in mid-November 2023. I want to continue my Spanish studies in Barcelona for another year, with the courses beginning in December.

To sum up:

1) My current Spanish student visa will expire in mid-November 2023.

2) I plan to apply for a new student visa in December.

3) I still hold a tourist Schengen visa until November 2024.

The problem is that there is a period of 30-35 days between two student visas. Can any of you kindly clarify for me whether I can stay in Barcelona until the start of my courses without leaving (and that this period will be automatically covered by my tourist Schengen) or if I have to fly out of the Schengen zone when the first visa ends and come back using my tourist visa until I apply for a new student visa.

Thank you for your help!