fix(admin): read the AI quality summary once on the Coach page

`/admin/coach` mounts the AI quality card and the Coach feedback card,
and both read `GET /api/admin/ai-quality` with the same unwrap, under
two different query keys, so every open sent the request twice. The
feedback card now reads the quality card's cell.

src/components/admin/__tests__/coach-feedback-section.test.tsx

@@ -19,6 +19,7 @@ vi.mock("@tanstack/react-query", () => ({
 }));
 
 import { I18nProvider } from "@/lib/i18n/context";
+import { AiQualitySection } from "../ai-quality-section";
 import { CoachFeedbackSection } from "../coach-feedback-section";
 
 function render() {
@@ -138,3 +139,25 @@ describe("CoachFeedbackSection", () => {
     }
   });
 });
+
+describe("the Coach admin page's two quality cards", () => {
+  it("read one cache cell, so the page asks for the summary once", () => {
+    useQueryMock.mockReset().mockReturnValue({
+      isLoading: true,
+      isError: false,
+      data: null,
+    });
+    renderToStaticMarkup(
+      <I18nProvider initialLocale="en">
+        <AiQualitySection />
+        <CoachFeedbackSection />
+      </I18nProvider>,
+    );
+
+    const keys = useQueryMock.mock.calls.map(
+      ([options]) => (options as { queryKey: unknown }).queryKey,
+    );
+    expect(keys).toHaveLength(2);
+    expect(keys[1]).toEqual(keys[0]);
+  });
+});

src/components/admin/coach-feedback-section.tsx

@@ -51,7 +51,9 @@ export function CoachFeedbackSection() {
   const fmt = useFormatters();
 
   const query = useQuery({
-    queryKey: queryKeys.adminCoachFeedback(),
+    // The same read as the AI quality section beside it, so one request
+    // serves both cards.
+    queryKey: queryKeys.adminAiQuality(),
     queryFn: async () => {
       const data = await apiGet<{ summary: FeedbackSummary | null } | null>(
         "/api/admin/ai-quality",