Hi @Kolb, Jannik ,
Welcome to Q&A forum!
Is there any error message about this?
According to your description, the problem seems to be related to the API, but I checked the official documentation Send a sharing invitation and there recently is no update about this API. It may also be that there is a problem in the API call process. Due to the limited forum permissions, we recommend that you submit a service request. The support team over there has the correct escalation channel, they can involve more resource and investigate the behavior from back end as fast as possible. They also can check the behavior on your end remotely. For reference: Get support - Microsoft 365 admin | Microsoft Docs.
Good day!
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