Microsoft Entra Connect (Azure AD Connect) reads the on-premises AD DS schema to determine which attributes are available for synchronization. The hybrid administrator guidance states that after extending AD with new/custom attributes, you must refresh the directory schema in Entra Connect so the sync engine recognizes the new attributes; only then can you include them in the synchronization rules ("Customize synchronization options") for export to Microsoft Entra ID. Until a schema refresh occurs, queries from Azure (e.g., via Cloud Shell) will not surface those attributes because the connector does not know about them.
Thus, the first step is to run "Refresh directory schema" in Microsoft Entra Connect; afterwards you can map
/select the custom attributes in the sync rules and verify they flow to Microsoft Entra ID.