Consider using
Shared Drive to save videos there. It allows for up to
400,000 files and folders - a lot more space than My Drive . It might need to be enabled by Tech/Admin. Note that when you upload to Shared Drive, content is owned by the organization and not by you as an individual. Also, check permission settings to make sure you can share the videos with students. (Information on Shared Drives - https://support.google.com/a/answer/7212025?hl=en&ref_topic=7337266)