Draft: feat: extend EOF error handling to all client-side streamers

Relates to issue #6260 (closed)

This MR was created by Duo in Session 1124520

Changes

• Identify all client-side streamers that need EOF error handling implementation
• Extend the error handling pattern from MR !7137 (merged) to all client-side streamers
• Ensure consistent error message formatting across all streamers
• Add proper error handling for io.EOF errors by calling Recv() to get actual error status