@Sokoban, Thanks for posting in Q&A. From your description, it seems you want to do co-management enrollment for the existing Configuration Manager clients. But the device is not enrolled. If there's any misunderstanding, feel free to let us know.
From the information you provided, it seems dsregcmd /status show AzureADjoined shows NO. That means the Hybrid Azure Join is not successful. I notice you have rejoined again. Could you confirm if both the AzureADjoined ,Domainjoined and AuzreADPrt are yes now?
Meanwhile, please let us know if we use user credential to do the enrolment or device credential. For user credential, please ensure the login user has Intune license.
In addition, please check if we have followed the article as below to enable the co-management on the new SCCM server as well:
https://learn.microsoft.com/en-us/mem/configmgr/comanage/tutorial-co-manage-clients
Please check the above information and if there's any update, feel free to let us know.
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