@Nathanael FLOTTES, Thanks for posting in Q&A. From your description, it seems that the Autopilot object is being created but not connected to the machine record which is working well in Intune. Could you confirm if you are using the Task Sequence Template and Scripts in the following link to do this.
Note: Non-Microsoft link, just for the reference.
Based as I know, the device added into the dynamic group and the profile status will change from Unassigned to Assigning and finally to Assigned, it may take some time. If the enroll occurs before the device is ready, our issue can occur. You can check the profile assigned and the Intune enrolled time to confirm on this.
Hope the above information can help.
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