I'm having the same problem. Apparently chaining .fileImporter modifiers doesn't work in SwifUI. And this doesn't seem to be documented anywhere. I'm going to take the approach of using a single .fileImporter and a separate variable to control which file type/behavior to use.
I would love to see if anyone has any other suggestions for handling multiple file importer dialogs in a single app.
Topic:
UI Frameworks
SubTopic:
SwiftUI