@Neuber-Wacek, Julia, Thanks for posting in Q&A. From your description, it seems you are doing co-management enroll and get error. If there's any misunderstanding, feel free to let us know.
Based as I know, there are two paths to do co-management, could you let us know which path we use to do the enrollment?
https://learn.microsoft.com/en-us/mem/configmgr/comanage/quickstart-paths
As you mentioned, the user has Intune license, please ensure both Azure AD premium and Intune licenses are assigned.
Meanwhile, please ensure the automatic enrollment is configured correctly, MDM user scope is set as all or a group include the user. And MSM user scope is set as none.
https://learn.microsoft.com/en-us/mem/intune/enrollment/quickstart-setup-auto-enrollment
Please check the above information and if there's any update, feel free to let us know.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.