Unable to sign in managed Apple id in supervised device after Icloud subscription

The message you're describing occurs when a Managed Apple Account has a requirement that the user can only sign in to it as part of enrolling in an account-driven enrollment. When you say that the issue goes away when you remove the subscription, I think you're removing that requirement.

However I'm not entirely sure what you're referring to by "iCloud subscription". Is that the iCloud access management setting in Apple School Manager or Apple Business Manager? Is it Apple Business Essentials?

A couple background details that may help:

A device can only have one device management enrollment at a time.

An enrollment can be associated with a Managed Apple Account, which makes it an account-driven enrollment. This is locked in at enrollment time. If the enrollment is not account-driven, you can't add a Managed Apple Account to that enrollment. You'll have to unenroll and re-enroll the device to change to an account-driven enrollment.

We have a supervised device that is currently managed by a third-party MDM. There is a requirement to extend the iCloud storage for the Managed Apple ID on this device, so we purchased an Apple Business Essentials subscription.

However, according to Apple’s documentation (link), it states:

“Services included with Apple Business Essentials aren’t supported with an external device management service.”

We would like assistance in understanding this limitation in our scenario, where:

We only need the extra iCloud storage provided by Apple Business Essentials for the Managed Apple ID.

Is it possible to retain third-party MDM management while still applying the increased iCloud storage from Apple Business Essentials to the Managed Apple ID?

Note: We understand that account-driven user Enrollment can solve this