Add 'spawn new chat' feature that carries current context (like /rewind does)

Claude Code has /rewind to restore conversation state at earlier checkpoints. This proves the system can checkpoint and restore context. However, there's no way to spawn a new chat thread that includes the current conversation state—only to rewind within the same chat.

Why this matters

• Long conversations become unwieldy; starting fresh would help organize work
• Allows splitting a conversation into focused subtasks without losing context
• Consistent with the capability already proven by /rewind

Proposed behavior

A /spawn or "New chat with current context" command that:

1. Takes the current conversation up to this point
2. Creates a new chat thread
3. Includes all prior messages in the new chat's context

Current workaround

• Manual copy/paste of context
• Saving to memory (only persists for future sessions, not immediately)
• Using Agent tool (creates a subprocess, not a new chat)

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User insight: If the system can rewind/restore state via /rewind, it should be able to fork/spawn a new chat with that state. The infrastructure is already there.