feat(tui): add side questions for running flows

[DongyunZou]

Summary

• Add the Claude-style /btw command to the TUI.
• Capture a bounded runtime snapshot of flow, task, agent state, handovers, spending, and recent events.
• Answer asynchronously through a read-only, skill-free agent clone without touching the primary queue, sessions, monitor, or cycle.
• Add lifecycle cleanup, stale-response protection, tests, and documentation.

Validation

• uv run pre-commit run --all-files
• uv run pytest: 1688 passed, 70 skipped
• pnpm --dir docs build
• pnpm --dir docs check:anchors