Limit file access to team members only

Hello!

We are a school using Teams/Sharepoint to manage files. We have one team for the staff only. Now we want to make sure, that the students (which are also members of the organization, but not members of this Team) will under no circumstances be able to access those files.

The issue is, that teachers will create links to the files in order to put them into mails or as cross-links into other documents. It is not realistic that they will always limit the scope of the link, so probably they will choose "everybody in the organization" at least occasionally. Also, we want things to be as easy for the teachers as possible. They have to cope with a lot of information when they arrive new at the school, and learning about restricting the scope of links will definitely not be their priority.

Is there a way to make sure that only Team members (Owners and Members) can access files, but no other members of the organization - despite any sharing that occurs?

Thanks for your help!
Knut Leiß (Den Haag)