That's a definite error. You need to report that.
Takeout Transfer should copy all files that the user owns and is editor on (even if that's actually not what anyone wants. Remember the Takeout Transfer is never an actual transfer.
Nowadays I usually recommend using a Shared Drive as intermediate storage for doing a real transfer.
User creates a Shared Drive, and adds their external account as Manager. Then moves content into the SD with the school account, and then moves it out of the SD with the external account.
Unless the admin has explicitly disallowed this, it should work fine.
Drive Sharing settings, Shared Drives section.

That's necessary for the external user to gain access.
This following setting in Sharing Options is necessary for the external user to export the content.

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