artifact: core/router/src/main/kotlin/com/correx/core/router/RouterFacade.kt
purpose: Implement RouterFacade — the orchestrating entry point that loads state via RouterRepository, builds context via RouterContextBuilder, routes inference via InferenceRouter, and conditionally emits SteeringNoteAddedEvent via EventStore.
depends_on: task-011, task-012
non_goals: Implementing protocol types, WebSocket handler, or infrastructure wiring
done_when: RouterFacade.handleChat() returns RouterResponse with correct content and steeringEmitted flag for both CHAT and STEERING modes