feat(settings): a time-format preference and one home for insight pills

The clock format followed the UI language with no way out — an English
interface forced AM/PM everywhere. A new profile preference (automatic,
24-hour, 12-hour) feeds every formatter through the shared locale
context, persists on the user row and rides the profile endpoints. The
insight pill list in settings gains the same eye toggle the overview
tiles have, so ordering and visibility live in one place; the page-side
'manage detail pages' block folds into a link there. Includes the
locale bundles for both features and the regenerated API contract.

src/hooks/use-auth.ts

@@ -3,6 +3,8 @@
 import { useQuery, useMutation, useQueryClient } from "@tanstack/react-query";
 import { useRouter } from "next/navigation";
 import { queryKeys } from "@/lib/query-keys";
+import type { TimeFormatPreference } from "@/lib/format-locale";
+import { isTimeFormatPreference, storeTimeFormat } from "@/lib/time-format";
 
 export interface AuthUser {
   id: string;
@@ -36,6 +38,14 @@ export interface AuthUser {
    * "metric" in `fetchMe`.
    */
   unitPreference: "metric" | "imperial";
+  /**
+   * Hour-cycle display preference. AUTO follows the locale convention
+   * (en → AM/PM, de → 24h); H12 / H24 pin the cycle regardless of locale.
+   * Mirrored into localStorage by `fetchMe` so `useFormatters()` and the
+   * legacy `src/lib/format.ts` helpers render the same clock. Coerced to
+   * "AUTO" against a stale /me payload.
+   */
+  timeFormat: TimeFormatPreference;
   /**
    * v1.4.47 W3 — per-user Coach opt-out. When `true`, every Coach
    * mount point (`<LayoutCoachFab>`, `<LayoutCoachMount>`, the
@@ -81,12 +91,22 @@ async function fetchMe(): Promise<AuthUser> {
     role: string;
     timezone: string;
   };
+  // Hour-cycle preference: coerce against a stale /me payload, then mirror
+  // into localStorage so `useFormatters()` and the legacy format helpers
+  // (which cannot reach the query cache) render the same clock.
+  const timeFormat: TimeFormatPreference = isTimeFormatPreference(
+    data.timeFormat,
+  )
+    ? data.timeFormat
+    : "AUTO";
+  storeTimeFormat(timeFormat);
   return {
     ...(data as AuthUser),
     disableCoach: data.disableCoach ?? false,
     // v1.7.0 — coerce against a stale /me payload (older server image
     // without the field) so the display defaults to metric.
     unitPreference: data.unitPreference === "imperial" ? "imperial" : "metric",
+    timeFormat,
     // v1.15.0 — coerce against a stale /me payload so the cycle nav entry
     // stays hidden by default when the field is absent.
     cycleTrackingEnabled: data.cycleTrackingEnabled === true,