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The SQL Backup Agent service runs as a Windows service, and communicates almost exclusively (more on that later) with the SQL Server instance running on the same machine. This is done via the use of interprocess-communication objects (IPC) and local SQL Server connections, hence no ports are actually required/used by the SQL Backup Agent service.
When you use the SQL Backup GUI, the GUI first connects to the SQL Server instance, which in turn communicates with the SQL Backup Agent service via IPC objects. There is no direct communication between 'outside' components and the SQL Backup Agent service.
The only exception is when your backup job is set to upload the backup file to a cloud storage provider (Amazon, Azure, etc). An external process (SQBHostedStorageClient.exe) is started by the SQL Backup Agent service to perform the upload. That is the only situation I know of where you can measure the bandwidth consumed by the SQL Backup Agent service (indirectly, since it's actually consumed by the uploader).