Format the panel and admin date and clock in the stored application timezone

The panel snapshot now carries the admin-saved `timezone` ("" when unset);
the coordinator threads it onto the household due-today sensor, and the
Party Board and Quest Log cards format their kicker, header and dock
date and clock in it, falling back to Home Assistant's zone only when
none is stored. The admin app loads the stored zone once
(AppTimezoneProvider) and uses it for completion clocks, History day
grouping, clocks and lateness, and "today" in Schedule, History and new
task defaults; Settings publishes a saved zone app-wide at once.

Resolves review finding TZ-001 (task 7e173881).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

admin/src/history/HistoryTab.test.tsx

@@ -5,6 +5,7 @@ import type { HistoryFilter, HistoryRow } from "../api/history";
 import { storeTokens } from "../auth/oidc";
 import { TransitionsProvider } from "../api/useTransitions";
 import { frame, testStream, type TestStream } from "../api/testStream";
+import { AppTimezoneProvider } from "../time/AppTimezone";
 
 const TODAY = "2026-09-23";
 
@@ -629,3 +630,114 @@ describe("HistoryTab live updates", () => {
     expect(screen.getAllByTestId("history-row")).toHaveLength(ROWS.all.length);
   });
 });
+
+describe("HistoryTab in the stored application timezone", () => {
+  // 13:00 UTC on Sep 23 is 01:00 on Sep 24 in Auckland (NZST, UTC+12).
+  const NOW = new Date("2026-09-23T13:00:00Z");
+  // Due 00:10 Auckland on Sep 24, done 00:30 Auckland (12:30 UTC on Sep 23).
+  const LATE_NZ = row({
+    instance_id: 7,
+    quest_title: "Feed cat",
+    due_date: "2026-09-24",
+    due_time: "00:10",
+    occurred_at: "2026-09-23T12:30:00Z",
+    was_on_time: false,
+  });
+  // 22:00 Auckland on Sep 23; 10:00 UTC.
+  const EVENING_NZ = row({ instance_id: 8, occurred_at: "2026-09-23T10:00:00Z" });
+
+  let fetchMock: ReturnType<typeof vi.fn>;
+
+  function historyRequests(): URL[] {
+    return fetchMock.mock.calls
+      .map(([url]) => new URL(String(url), "http://x"))
+      .filter((url) => url.pathname === "/api/v1/admin/history");
+  }
+
+  async function renderWithZone(timezone: string) {
+    fetchMock = vi.fn((url: string) => {
+      const parsed = new URL(url, "http://x");
+      if (parsed.pathname.endsWith("/api/v1/admin/settings")) {
+        return Promise.resolve(jsonResponse({ timezone }));
+      }
+      const filter = parsed.searchParams.get("filter");
+      const rows = filter === "all" ? [EVENING_NZ, LATE_NZ] : [];
+      return Promise.resolve(
+        jsonResponse({
+          filter,
+          start: parsed.searchParams.get("start"),
+          end: parsed.searchParams.get("end"),
+          count: rows.length,
+          rows,
+        }),
+      );
+    });
+    vi.stubGlobal("fetch", fetchMock);
+    render(
+      <AppTimezoneProvider>
+        <HistoryTab />
+      </AppTimezoneProvider>,
+    );
+    await screen.findByTestId("stat-on-time");
+  }
+
+  function times(section: HTMLElement): string[] {
+    return Array.from(section.querySelectorAll(".history-event-time")).map(
+      (el) => el.textContent ?? "",
+    );
+  }
+
+  beforeAll(() => {
+    vi.stubEnv("TZ", "UTC");
+  });
+
+  afterAll(() => {
+    vi.unstubAllEnvs();
+  });
+
+  beforeEach(() => {
+    sessionStorage.clear();
+    storeTokens({ access_token: "at-123", expires_in: 600 });
+    vi.useFakeTimers({ toFake: ["Date"], now: NOW });
+  });
+
+  afterEach(() => {
+    cleanup();
+    vi.useRealTimers();
+    vi.unstubAllGlobals();
+  });
+
+  it("today, day grouping, clock and lateness follow the stored zone", async () => {
+    await renderWithZone("Pacific/Auckland");
+
+    for (const url of historyRequests()) {
+      expect(url.searchParams.get("end")).toBe("2026-09-24");
+      expect(url.searchParams.get("start")).toBe("2026-09-11");
+    }
+    const today = screen.getByTestId("day-2026-09-24");
+    expect(within(today).getByText("Today")).toBeTruthy();
+    expect(times(today)).toEqual(["12:30 AM"]);
+    expect(metas(today)).toEqual(["completed · panel (Declan) · late 20 min"]);
+
+    const yesterday = screen.getByTestId("day-2026-09-23");
+    expect(within(yesterday).getByText("Yesterday")).toBeTruthy();
+    expect(times(yesterday)).toEqual(["10:00 PM"]);
+  });
+
+  it("an empty stored zone keeps the browser's local day and clock", async () => {
+    await renderWithZone("");
+
+    for (const url of historyRequests()) {
+      expect(url.searchParams.get("end")).toBe("2026-09-23");
+    }
+    expect(screen.queryByTestId("day-2026-09-24")).toBeNull();
+    const today = screen.getByTestId("day-2026-09-23");
+    expect(within(today).getByText("Today")).toBeTruthy();
+    expect(times(today)).toEqual(["12:30 PM", "10:00 AM"]);
+    // Due 00:10 UTC on Sep 24 is after the 12:30 UTC completion: no minutes.
+    expect(metas(today)).toEqual([
+      "completed · panel (Declan) · late",
+      "completed · panel (Declan) · on time",
+    ]);
+  });
+});