Improve the integration with the GH Coding Agent

[rebornix]

Users can interact with the GitHub Coding Agent (Padawan) in VS Code today using the GitHub Pull Request and Issues extension. They can assign issues to Padawan, view PRs it creates, and visit streaming log links from PR descriptions. However, users cannot yet track detailed progress, manage Padawan sessions, or easily switch between Padawan workflows and Copilot Chat in VS Code.

Our goal is to improve the integration with the GitHub Coding Agent in VS Code by enabling users to:

• Manage and monitor Padawan tasks in VS Code
  • Start Padawan tasks from Copilot Chat (leveraging the history/context of the current chat session)
    • Currently users can start Padawan tasks by assigning an issue to Copilot or using @github Create a PR to ... in Chat
  • Track the progress of Padawan tasks
    • Users can view ongoing Padawan tasks in VS Code (currently shown in "Copilot on My Behalf" section)
    • Users can view session logs directly in VS Code (similar to web session logs)
    • Users can get notified when a Padawan task is started, completed, or fails
    • Transition seamlessly between Task view, Session logs, and PR view
  • Check out PRs created by Padawan and bootstrap Chat Agent session
    • Padawan task context is included in the new chat session
• Explore bringing Copilot Agents command center into VS Code
• Share instruction.md files between Padawan and vscode