refactor(workouts): render workout dates through useFormatters

The workout list, the workout detail header and the dashboard's recent
workouts tile each rebuilt their own date formatter from the shared
cache, with a private copy of the current-year check, and so ignored
the reader's date-order preference. They now use useFormatters(), and
the copies are gone.

The timezone formatter guard now refuses any two-argument
getDateTimeFormat call in src/components, so a component cannot build
its own display formatter again. The medication card's day bucketing,
the one other such call, reads userDayKey instead.

src/components/dashboard/__tests__/recent-workouts-tile.test.tsx

@@ -2,6 +2,7 @@ import { describe, it, expect, vi, beforeEach } from "vitest";
 import { renderToStaticMarkup } from "react-dom/server";
 
 import { I18nProvider } from "@/lib/i18n/context";
+import { makeFormatters } from "@/lib/format-locale";
 import type { WorkoutListEntry } from "@/hooks/use-workouts";
 
 /**
@@ -17,6 +18,13 @@ vi.mock("@/hooks/use-auth", () => ({
   useAuth: () => ({ isAuthenticated: true }),
 }));
 
+// The day label follows the reader's date order through `useFormatters()`.
+const READER_FORMATTERS = makeFormatters("en", "UTC", "H24", "YMD");
+vi.mock("@/lib/i18n/context", async (importOriginal) => ({
+  ...(await importOriginal<typeof import("@/lib/i18n/context")>()),
+  useFormatters: () => READER_FORMATTERS,
+}));
+
 let mockResult: {
   data:
     | {
@@ -147,5 +155,8 @@ describe("<RecentWorkoutsTile>", () => {
     expect(html).toContain("Cycling");
     expect(html).toContain("30m");
     expect(html).toContain("1h 0m");
+    expect(html).toContain(
+      READER_FORMATTERS.dateWithWeekdaySmart("2026-05-15T07:00:00Z"),
+    );
   });
 });

src/components/dashboard/recent-workouts-tile.tsx

@@ -4,12 +4,11 @@ import Link from "next/link";
 import { Activity } from "lucide-react";
 
 import { formatDurationMinutes } from "@/lib/i18n/duration";
-import { useDisplayTimezone, useTranslations } from "@/lib/i18n/context";
+import { useFormatters, useTranslations } from "@/lib/i18n/context";
 import { useWorkouts, type WorkoutListEntry } from "@/hooks/use-workouts";
 import { cn } from "@/lib/utils";
 import { Card, CardContent, CardHeader } from "@/components/ui/card";
 import { TileHeader } from "@/components/insights/tile-header";
-import { getDateTimeFormat } from "@/lib/intl/formatter-cache";
 import { Skeleton } from "@/components/ui/skeleton";
 import { QueryErrorCard } from "@/components/ui/query-error-card";
 import { iconForSport } from "@/lib/workouts/sport-icons";
@@ -32,16 +31,6 @@ import { iconForSport } from "@/lib/workouts/sport-icons";
  * round-trip per session.
  */
 
-function formatDayLabel(iso: string, locale: string, timeZone: string): string {
-  const d = new Date(iso);
-  return getDateTimeFormat(locale, {
-    timeZone,
-    weekday: "short",
-    day: "2-digit",
-    month: "short",
-  }).format(d);
-}
-
 function renderRow(workout: WorkoutListEntry, sportName: string) {
   const Icon = iconForSport(workout.sportType);
   return (
@@ -61,8 +50,8 @@ function renderRow(workout: WorkoutListEntry, sportName: string) {
 }
 
 export function RecentWorkoutsTile() {
-  const { t, locale } = useTranslations();
-  const timeZone = useDisplayTimezone();
+  const { t } = useTranslations();
+  const fmt = useFormatters();
   const { data, isError, error, refetch } = useWorkouts({ limit: 3 });
 
   // A query's `isLoading` is not a hydration-safe branch: TanStack reports the
@@ -148,7 +137,7 @@ export function RecentWorkoutsTile() {
                   >
                     {renderRow(workout, sportName)}
                     <span className="text-muted-foreground shrink-0 text-xs tabular-nums">
-                      {formatDayLabel(workout.startedAt, locale, timeZone)}
+                      {fmt.dateWithWeekdaySmart(workout.startedAt)}
                     </span>
                     <span className="ml-1 shrink-0 text-xs font-medium tabular-nums">
                       {formatDurationMinutes(