Apparently, the following does provide a solution:
- Go to library settings, advanced settings, enable management of content types.
- Check, which content types have the additional email columns.
- Option 1: Set the email columns from Optional to Hidden.
- Option 2: Delete the existing content types and add them again from site content types.
- In content type, enable displaying the property panel in office.
- Test again, it is now possible to edit emailed documents in office.
I think self-proposing answers is frowned upon, so I'll leave this issue open and wait for confirmation.
Kind regards,
Adrian
Update: Instead of recreating the content type, it is also possible to solve the issue by setting the Email columns to Hidden. Thanks, Nico!