A cloud-based identity and access management service for securing user authentication and resource access
This appears to be an object matching problem. Since the users already exist in Entra ID from your previous Exchange Online migration, Entra Connect is trying to create or join the on-premises AD objects with existing cloud objects. The ProxyAddresses conflict indicates that another Entra ID object already owns the same SMTP address, so Entra Connect cannot complete the join.
Removing the proxy address from AD works because it removes the conflict, but it causes Entra Connect to create a new cloud object because the existing Entra object is not being matched correctly. To fix this, hard match the existing Entra ID user with the on-premises AD user by setting the cloud user's ImmutableID to the Base64-encoded objectGUID of the AD account before enabling synchronization.
For details, refer to https://michev.info/blog/post/6129/how-to-hard-match-entra-id-users-via-the-graph-api-or-the-graph-sdk-for-powershell
If this was done and it still failed, verify that you used the correct AD object's objectGUID, that the ImmutableID was actually applied, and that no other Entra object already has the same proxy address.
Also check for duplicate objects in Entra ID (especially guest users, soft-deleted users, or previously migrated accounts) that may hold the same proxyAddresses value. You can verify this with Microsoft Graph PowerShell or Entra admin center searches for the SMTP address.
For your goal of having on-premises AD as the password source, you need to configure Entra Connect with Password Hash Synchronization (PHS). After the users are correctly matched and synchronized, password changes made in on-premises AD will be synchronized to Microsoft 365, giving users a single password experience. You do not need Exchange hybrid for this; Exchange Online can remain cloud-only while AD remains the identity source.
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hth
Marcin