refactor: improve error logging in ClineProvider

[samhvw8]

• Replace console.error with outputChannel.appendLine for better error visibility
• Add detailed error information using JSON.stringify with full error properties
• Improve error message formatting and consistency across all error handlers

With this PR, User can report with output log

Description

Type of change

• Bug fix (non-breaking change which fixes an issue)
• New feature
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

How Has This Been Tested?

Checklist:

• My code follows the patterns of this project
• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation

Additional context

Related Issues

Reviewers

---

Important

Refactor ClineProvider to enhance error logging by using outputChannel.appendLine and JSON.stringify for detailed and consistent error messages.

• Error Logging:
  • Replace console.error with outputChannel.appendLine in ClineProvider for better error visibility.
  • Use JSON.stringify to include full error properties in logs for detailed error information.
  • Improve error message formatting for consistency across all error handlers in ClineProvider.

^{This description was created by for 17c0dea. It will automatically update as commits are pushed.}

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