[VS Code Extension] Preserve input text across session navigation + multi-agent management

Bug: Input text lost when switching between sessions

Steps to reproduce:

1. Open the Claude Code VS Code extension with multiple sessions running
2. Start typing a message in the input box of Session A
3. Switch to Session B to check its progress
4. Switch back to Session A

Expected: Draft text is preserved in the input box
Actual: The typed text is gone — the input box is empty

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Feature Request: Better multi-agent session management

Managing multiple concurrent Claude Code agents in VS Code is awkward compared to how Copilot handles parallel agent tasks. Would love to see:

• A session list/panel showing all running agents with their current status (running, waiting, done)
• Ability to name/label sessions
• Visual indicator of which sessions need attention (e.g. waiting for input)
• Quick switching between sessions without losing input state

This would make it much easier to parallelize work across multiple agents the way power users tend to operate.