feat(coach): make launch scope visible and seed the blank state

Replace the hidden composer prefill with a visible scope affordance: when
the Coach is launched narrowed to a metric, the hero shows a scope pill
naming that metric plus a tappable seed question, and the drawer sources
rail surfaces the same scope line. When the Coach opens unscoped, resolve
today's most notable derived signal server-side and offer it as a tappable
opener; fall back to the neutral greeting when no signal crosses the gate,
so the blank box is never cold and never fabricated.

Add an internal GET /api/insights/coach/seeded-question that reuses the
briefing's derived-signal detector to select the opener server-side; the
client renders the resolved DTO.

src/lib/query-keys/coach.ts

@@ -26,4 +26,10 @@ export const coachKeys = {
    * the streaming hook invalidates this slot once the persisted twin lands.
    */
   coachConversation: (id: string | null) => ["coachConversation", id] as const,
+  /**
+   * v1.22.0 (A3) — today's most notable derived signal, resolved into the
+   * Coach hero's pre-seeded relevance opener
+   * (`GET /api/insights/coach/seeded-question`).
+   */
+  coachSeededQuestion: () => ["coach-seeded-question"] as const,
 };