Story-1665 — Dock WS streaming: real Atlas dock_chat turn

0. The defect this closes

The Agent Dock on every workspace page LOOKED live but FAKED its answer. On send, agent-dock-mount.tsx POSTed the /session-context/resolve authority handshake and then appended a canned i18n string — turnResolved: "Got your message — I'm oriented on this page and ready." — as if it were Atlas. The brain (AgentCore) was never invoked: zero service.name=atlas Dock spans in Logfire. The component doc admitted it: "the brain's streamed reply … is a distinct runtime boundary not wired here."

1. What this Story wires

The Dock's send now launches a real kind:"dock_chat" turn over the ADR-110 broker WebSocket and streams Atlas's answer into the thread. The producers it depends on are already on main: the contract kind/DockChatContext (#1663), the broker routing (#1660), the Atlas dock-chat brain (#1664), and the synced src/gen (#1669).

The rail flow

composer send
  → useDockChatRail.send(text)
  → AgentRailConnection (shared transport; dock launch builder)
  → WS { agentKey:"atlas_dock_chat", kind:"dock_chat",
         dockChat:{ surface_key, available_surfaces, granted_permissions,
                    current_context, counsel_message, thinking_level } }
  → broker routes on kind → AgentCore Atlas dock_chat (#1664)
  → frames: run.accepted → turn.delta* → turn.completed → run.done
  → reduceFrame → streamingMessageMd (live bubble) → committed reply in thread
  → navigate_to (if any) → confirm-first nav chip (dispatcher, never auto-route)

2. Shared, not forked

The wizard intake rail and the Dock chat rail are now the same module-scoped connection machinery (atlas-rail-store) — the hard-won reconnect / watchdog / StrictMode-survival logic (Story-1373) is reused, not duplicated. The only agent-specific bit is the launch/query message, injected as a builder. The wizard path is byte-unchanged (its tests pass untouched).

3. Trust boundary (RFC-APB-002)

The DockChatContext blocks (available_surfaces, granted_permissions, current_context) are orientation only. The broker re-resolves real authority from the Clerk session on the socket — a forged client context grants nothing. Browser context never becomes authority.

4. Verification

• ✓ tsc --noEmit — 0 errors in src/
• ✓ pnpm lint
• ✓ pnpm test (agent rail + dock; wizard rail tests unchanged + green)
• ✓ pnpm build
• ▲ Live seam (ADR-110): the close gate is a real streamed answer on staging + a fresh service.name=atlas dock_chat trace in Logfire — proven in the deploy step, NOT by this green build. Requires the functions Lambda + agents AgentCore deploys (producers) live first.
• ▲ Known orphan: use-agent-live-rail.ts (the HTTP resolve handshake) is no longer used by the Dock. Left in place — it may be the server-plane authz seam; removal is a separate cleanup once that's confirmed.