feat(client): add offline mode banner indicator

Displays a prominent banner at the top of all pages when the user
is offline, informing them that changes will sync when reconnected.
Shows pending change count when applicable.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

5 files changed, 149 insertions, 21 deletions

diff --git a/docs/dev/roadmap.md b/docs/dev/roadmap.md
index ac0760e..c9c000f 100644
--- a/docs/dev/roadmap.md
+++ b/docs/dev/roadmap.md
@@ -165,7 +165,7 @@ Smaller features first to enable early MVP validation.
 ### Sync UI
 - [x] Sync status indicator
 - [x] Manual sync button
-- [ ] Offline mode indicator
+- [x] Offline mode indicator
 
 **✅ Milestone**: Study offline and sync when back online
 
diff --git a/src/client/App.tsx b/src/client/App.tsx
index f774003..3c20c54 100644
--- a/src/client/App.tsx
+++ b/src/client/App.tsx
@@ -1,5 +1,5 @@
 import { Route, Switch } from "wouter";
-import { ProtectedRoute } from "./components";
+import { OfflineBanner, ProtectedRoute } from "./components";
 import {
 	DeckDetailPage,
 	HomePage,
@@ -10,24 +10,27 @@ import {
 
 export function App() {
 	return (
-		<Switch>
-			<Route path="/">
-				<ProtectedRoute>
-					<HomePage />
-				</ProtectedRoute>
-			</Route>
-			<Route path="/decks/:deckId">
-				<ProtectedRoute>
-					<DeckDetailPage />
-				</ProtectedRoute>
-			</Route>
-			<Route path="/decks/:deckId/study">
-				<ProtectedRoute>
-					<StudyPage />
-				</ProtectedRoute>
-			</Route>
-			<Route path="/login" component={LoginPage} />
-			<Route component={NotFoundPage} />
-		</Switch>
+		<>
+			<OfflineBanner />
+			<Switch>
+				<Route path="/">
+					<ProtectedRoute>
+						<HomePage />
+					</ProtectedRoute>
+				</Route>
+				<Route path="/decks/:deckId">
+					<ProtectedRoute>
+						<DeckDetailPage />
+					</ProtectedRoute>
+				</Route>
+				<Route path="/decks/:deckId/study">
+					<ProtectedRoute>
+						<StudyPage />
+					</ProtectedRoute>
+				</Route>
+				<Route path="/login" component={LoginPage} />
+				<Route component={NotFoundPage} />
+			</Switch>
+		</>
 	);
 }
diff --git a/src/client/components/OfflineBanner.test.tsx b/src/client/components/OfflineBanner.test.tsx
new file mode 100644
index 0000000..41679d9
--- /dev/null
+++ b/src/client/components/OfflineBanner.test.tsx
@@ -0,0 +1,85 @@
+/**
+ * @vitest-environment jsdom
+ */
+import "fake-indexeddb/auto";
+import { cleanup, render, screen } from "@testing-library/react";
+import { afterEach, beforeEach, describe, expect, it, vi } from "vitest";
+import { OfflineBanner } from "./OfflineBanner";
+
+// Mock the useSync hook
+const mockUseSync = vi.fn();
+vi.mock("../stores", () => ({
+	useSync: () => mockUseSync(),
+}));
+
+describe("OfflineBanner", () => {
+	beforeEach(() => {
+		vi.clearAllMocks();
+	});
+
+	afterEach(() => {
+		cleanup();
+	});
+
+	it("renders nothing when online", () => {
+		mockUseSync.mockReturnValue({
+			isOnline: true,
+			pendingCount: 0,
+		});
+
+		render(<OfflineBanner />);
+
+		expect(screen.queryByTestId("offline-banner")).toBeNull();
+	});
+
+	it("renders banner when offline", () => {
+		mockUseSync.mockReturnValue({
+			isOnline: false,
+			pendingCount: 0,
+		});
+
+		render(<OfflineBanner />);
+
+		const banner = screen.getByTestId("offline-banner");
+		expect(banner).toBeDefined();
+		expect(
+			screen.getByText(/You're offline. Changes will sync when you reconnect./),
+		).toBeDefined();
+	});
+
+	it("displays pending count when offline with pending changes", () => {
+		mockUseSync.mockReturnValue({
+			isOnline: false,
+			pendingCount: 5,
+		});
+
+		render(<OfflineBanner />);
+
+		expect(screen.getByTestId("offline-pending-count")).toBeDefined();
+		expect(screen.getByText("(5 pending)")).toBeDefined();
+	});
+
+	it("does not display pending count when there are no pending changes", () => {
+		mockUseSync.mockReturnValue({
+			isOnline: false,
+			pendingCount: 0,
+		});
+
+		render(<OfflineBanner />);
+
+		expect(screen.queryByTestId("offline-pending-count")).toBeNull();
+	});
+
+	it("has correct accessibility attributes", () => {
+		mockUseSync.mockReturnValue({
+			isOnline: false,
+			pendingCount: 0,
+		});
+
+		render(<OfflineBanner />);
+
+		const banner = screen.getByTestId("offline-banner");
+		expect(banner.getAttribute("role")).toBe("status");
+		expect(banner.getAttribute("aria-live")).toBe("polite");
+	});
+});
diff --git a/src/client/components/OfflineBanner.tsx b/src/client/components/OfflineBanner.tsx
new file mode 100644
index 0000000..357db33
--- /dev/null
+++ b/src/client/components/OfflineBanner.tsx
@@ -0,0 +1,39 @@
+import { useSync } from "../stores";
+
+export function OfflineBanner() {
+	const { isOnline, pendingCount } = useSync();
+
+	if (isOnline) {
+		return null;
+	}
+
+	return (
+		<div
+			data-testid="offline-banner"
+			role="status"
+			aria-live="polite"
+			style={{
+				backgroundColor: "#6c757d",
+				color: "white",
+				padding: "0.5rem 1rem",
+				textAlign: "center",
+				fontSize: "0.875rem",
+				display: "flex",
+				alignItems: "center",
+				justifyContent: "center",
+				gap: "0.5rem",
+			}}
+		>
+			<span aria-hidden="true">⚡</span>
+			<span>
+				You're offline. Changes will sync when you reconnect.
+				{pendingCount > 0 && (
+					<span data-testid="offline-pending-count">
+						{" "}
+						({pendingCount} pending)
+					</span>
+				)}
+			</span>
+		</div>
+	);
+}
diff --git a/src/client/components/index.ts b/src/client/components/index.ts
index 31ebe1f..10f31c6 100644
--- a/src/client/components/index.ts
+++ b/src/client/components/index.ts
@@ -1,3 +1,4 @@
+export { OfflineBanner } from "./OfflineBanner";
 export { ProtectedRoute } from "./ProtectedRoute";
 export { SyncButton } from "./SyncButton";
 export { SyncStatusIndicator } from "./SyncStatusIndicator";