Benjamin,
Chris' method should work but I have another possibility I also want to share. Files cannot be section specific and neither can Page or Modules. But Assignments can. And Assignments don't have to really be Assignments that are graded. So one idea is to create Assignments assigned to each section and link to the files/data sets within the Assignment. You can set Display Grade As to Not Graded and then you won't get a column in the gradebook either.
The above method makes it so that students should see links only to the files that for the Assignments assigned to them. This will work as long as you keep Files hidden on the left side navigation. If you don't want to hide it you can also set a permission on the data set file so that they are only available from links and not from directly under Files.
Here are a couple more links which might be useful with what I describe above.
How do I assign an assignment to a course section?
How do I restrict files and folders to students in Canvas?
Let me know if this doesn't make sense and I can create some examples in screenshots or a video.
Rick
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