For the issue of your device your device not showing as Microsoft Intune MDM Registered, it sounds like the Intune registration is not completing. In order for the Intune registration to complete, the user enrolling the device needs to have a Microsoft Intune license and Azure AD Premium license. In the automatic enrollment configuration the "MDM user scope" needs to be set to "ALL" and the "MAM user scope" needs to be set to "none". (Otherwise the MAM user scope will take precedence.)
For the duplicate device issue, when a device is connected to Entra as Microsoft Entra Registered due to a user selecting "Add account to Windows", and you enable Microsoft Entra Joined, the device will be connected twice to Entra, and you will see two different computer objects for the same device name. This is documented in the FAQ: https://learn.microsoft.com/en-us/entra/identity/devices/faq#why-do-i-see-a-duplicate-microsoft-entra-registered-record-for-my-windows-10-11-microsoft-entra-hybrid-joined-device-in-the-microsoft-entra-devices-list
This dual state issue can be caused by old device records existing in Entra, and can be resolved by deleting the device in Intune and deleting all records of the affected devices in Entra, and then re-enrolling the devices. If your devices change names then they could appear multiple times.
If you still run into this issue, feel free to send me an email at AzCommunity@microsoft.com ("Attn: Marilee Turscak") and include your subscription ID and a link to this thread, and I can enable a one-time free support case to help look into this issue.
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