Hi Tansu,
Thank you for explaining the situation.
Your Gmail account and your university account are two separate Microsoft accounts, each with its own OneDrive storage. Therefore, a Microsoft 365 Education licence assigned to your university account generally cannot be transferred to or used to increase the storage of your Gmail-linked OneDrive.
Also, university email is managed directly by your institution's administrator. The university’s Microsoft 365 administrator controls the account, licence, storage allocation, access, etc., so normally you can't use the school email to purchase a Microsoft 365 subscription yourself.
Please sign in to My Account separately with your Gmail address and your university address, then check the exact subscription name and which account currently owns it. With this information, I can help provide the best next step in your case.
Looking forward to hearing from you soon.