Clean up Connection and Sync Input/Output stream classes

The classes `Connection` and `SyncInputSream`/`SyncOutputStream` have a bunch of methods that contain business logic for sync. This is not a good place for that logic to live. We should transfer the sync specific logic into helper static methods and colocate those methods with the sync code.

Locate the Connection, SyncInputSream, and SyncOutputStream classes and identify the methods containing synchronization business logic. Trace the existing sync code to determine where helper static methods should be colocated; done means the sync-specific logic has moved out of the stream classes without changing their behavior.

Written by the indexing model from the issue text.