Hi Claus Kesting,
For Fill forms, you should choose Add an existing formand then select a form you want to fill when you create the Form. Rather than "Create a shared form that your team can edit and see results"
Then you will see it as following:
For your reference: https://support.office.com/en-us/article/create-edit-and-collaborate-on-a-form-in-microsoft-teams-333b97a3-41d9-48bc-a1cb-84a96bd44e14
Thanks,
Iry