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/App.test.tsx

@@ -2,10 +2,28 @@ import { afterEach, beforeEach, describe, expect, it, vi } from "vitest";
 import { cleanup, fireEvent, render, screen } from "@testing-library/react";
 import App from "./App";
 
+function jsonResponse(body: unknown, status = 200): Response {
+  return new Response(JSON.stringify(body), {
+    status,
+    headers: { "Content-Type": "application/json" },
+  });
+}
+
+let settingsResponse: () => Promise<Response>;
+
 describe("NestQuest Admin shell", () => {
   beforeEach(() => {
-    // The Today tab fetches the admin snapshot; keep the shell tests offline.
-    vi.stubGlobal("fetch", vi.fn(() => new Promise<Response>(() => {})));
+    settingsResponse = () => Promise.resolve(jsonResponse({ timezone: "" }));
+    // The shell loads the stored application timezone; every tab's own
+    // requests stay pending so the shell tests remain offline.
+    vi.stubGlobal(
+      "fetch",
+      vi.fn((url: string) =>
+        String(url).endsWith("/api/v1/admin/settings")
+          ? settingsResponse()
+          : new Promise<Response>(() => {}),
+      ),
+    );
   });
 
   afterEach(() => {
@@ -22,10 +40,10 @@ describe("NestQuest Admin shell", () => {
     }
   });
 
-  it("starts on the Today screen and switches on tab click", () => {
+  it("starts on the Today screen and switches on tab click", async () => {
     render(<App />);
 
-    expect(screen.getByRole("heading", { name: "Today" })).toBeTruthy();
+    expect(await screen.findByRole("heading", { name: "Today" })).toBeTruthy();
 
     fireEvent.click(screen.getByRole("tab", { name: "History" }));
 
@@ -36,12 +54,33 @@ describe("NestQuest Admin shell", () => {
     );
   });
 
-  it("the Tasks tab renders the definitions screen", () => {
+  it("the Tasks tab renders the definitions screen", async () => {
     render(<App />);
 
     fireEvent.click(screen.getByRole("tab", { name: "Tasks" }));
 
-    expect(screen.getByRole("heading", { name: "Tasks" })).toBeTruthy();
+    expect(await screen.findByRole("heading", { name: "Tasks" })).toBeTruthy();
     expect(screen.getByRole("tabpanel").textContent).not.toContain("placeholder");
   });
-});
+
+  it("renders no screen until the stored application timezone is known", async () => {
+    settingsResponse = () => new Promise<Response>(() => {});
+    render(<App />);
+
+    expect(screen.getByTestId("timezone-loading")).toBeTruthy();
+    expect(screen.queryByRole("heading", { name: "Today" })).toBeNull();
+  });
+
+  it("a failed timezone load says so and retries", async () => {
+    settingsResponse = () => Promise.resolve(jsonResponse({ detail: "boom" }, 500));
+    render(<App />);
+
+    await screen.findByTestId("timezone-error");
+    expect(screen.queryByRole("heading", { name: "Today" })).toBeNull();
+
+    settingsResponse = () => Promise.resolve(jsonResponse({ timezone: "Pacific/Auckland" }));
+    fireEvent.click(screen.getByRole("button", { name: "Try again" }));
+
+    expect(await screen.findByRole("heading", { name: "Today" })).toBeTruthy();
+  });
+});