The two Azure services to use for migrating 20 TB of on-premises network share data with bandwidth management for repeated transfers after the initial sync are Azure Data Box and Azure File Sync.
Azure Data Box is used for the initial bulk data transfer of the 20 TB to Azure. This physical appliance-based approach accelerates the movement of large data volumes by shipping a secure, proprietary storage device to your data center. This bypasses the limitations of network bandwidth for the initial large data copy, making the process faster and more cost-effective than a pure online transfer.
Azure Storage Mover: For data sources that change frequently, Storage Mover can work with Data Box to transfer initial bulk data, then catch up on just the delta (new/changed files or metadata).
This combined approach, often referred to as an "offline data transfer with online sync" hybrid migration, ensures a fast initial migration with minimal disruption, followed by a continuous, controlled synchronization process with bandwidth management.
Reference:
https://learn.microsoft.com/en-us/azure/databox/data-box-overview