Users can now classify forms created via Microsoft Forms. The enhancement is currently in rollout, but the documentation is not yet available or published/updated.
Based on testing with my personal configuration, Forms supports labels with the Files scope, including encryption, but not user-defined permissions (only assigned permissions). If the feature is available in your tenant, the usual Sensitivity symbol appears in the Forms designer (in the top center), next to where the system saves the form.

Restricted forms display a banner for authors and co-authors, and collection settings are restricted accordingly.

Users also see the sensitivity label on the form.

Authors and co-authors can manually assign or edit sensitivity labels on forms, ensuring that only users with appropriate permissions can access the form design and response pages. Sensitivity labels are also inherited by Excel files generated from Forms, maintaining consistent data protection across exported content.

