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

Relates to issue #6260 (closed)

This MR was created by Duo in Session 1119776

Changes

• Extend proper EOF error handling pattern to all client-side streamers that don't use the Chunker pattern
• Implement consistent error handling by calling Recv() when io.EOF is encountered during Send() operations
• Ensure proper error propagation from server-side errors instead of returning opaque EOF errors
• Apply the pattern established in MR !7137 (merged) to remaining client-side streamers throughout the codebase