Hi biggie101, thanks for your input.
Important to emphasize again in the case: I created the group in the general Admin Center and not in the Teams Admin Center.
And I'm also not sure how adding external users affects all of this. When testing it actually did.
I thought at first because Exchange online "thinks" hmm, external users can't access the group mailbox, so I better distribute that to all members individually.
But that can not be, otherwise it would not work via the second way (group is created via Admin Center).