feat(example): add Expo example app with three demo screens

Demonstrates all three API styles and two real fintech use cases.

Screens:
- Session Timeout (index): primary fintech use case — 5-min session timer,
  persisted across app kills, customizable duration, Android notification config,
  permission check for exact alarms, onBackground/onForeground callbacks
- OTP Expiry (otp): 90-second OTP countdown using the hook API, shows
  urgency color transitions, persist: false since OTPs are ephemeral
- API Playground: three concurrent timers using hook / imperative /
  legacy setTimeout APIs simultaneously with live event logs

Components:
- TimerRing: animated circular progress ring with drift-aware color states
- StatusBadge: status + background indicator chip
- theme.ts: shared design tokens (slate/indigo dark theme)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: Richard

example/app.json

@@ -0,0 +1,42 @@
+{
+  "expo": {
+    "name": "BGTimerExample",
+    "slug": "bg-timer-example",
+    "version": "1.0.0",
+    "orientation": "portrait",
+    "icon": "./assets/icon.png",
+    "userInterfaceStyle": "automatic",
+    "scheme": "bgtimer",
+    "splash": {
+      "backgroundColor": "#0F172A"
+    },
+    "ios": {
+      "supportsTablet": false,
+      "bundleIdentifier": "com.rick427.bgtimer.example",
+      "infoPlist": {
+        "UIBackgroundModes": ["processing", "fetch"]
+      }
+    },
+    "android": {
+      "package": "com.rick427.bgtimer.example",
+      "adaptiveIcon": {
+        "backgroundColor": "#0F172A"
+      }
+    },
+    "plugins": [
+      "expo-router",
+      [
+        "@rick427/background-timer",
+        {
+          "taskIdentifiers": [
+            "com.rick427.bgtimer.example.session-timeout",
+            "com.rick427.bgtimer.example.otp-expiry"
+          ]
+        }
+      ]
+    ],
+    "experiments": {
+      "typedRoutes": true
+    }
+  }
+}

example/app/(tabs)/_layout.tsx

@@ -0,0 +1,47 @@
+import { Tabs } from 'expo-router';
+import { Ionicons } from '@expo/vector-icons';
+import { COLORS } from '../../src/theme';
+
+export default function TabLayout() {
+  return (
+    <Tabs
+      screenOptions={{
+        headerShown: false,
+        tabBarStyle: {
+          backgroundColor: COLORS.surface,
+          borderTopColor: COLORS.border,
+        },
+        tabBarActiveTintColor: COLORS.primary,
+        tabBarInactiveTintColor: COLORS.textMuted,
+      }}
+    >
+      <Tabs.Screen
+        name="index"
+        options={{
+          title: 'Session',
+          tabBarIcon: ({ color, size }) => (
+            <Ionicons name="shield-checkmark" size={size} color={color} />
+          ),
+        }}
+      />
+      <Tabs.Screen
+        name="otp"
+        options={{
+          title: 'OTP',
+          tabBarIcon: ({ color, size }) => (
+            <Ionicons name="keypad" size={size} color={color} />
+          ),
+        }}
+      />
+      <Tabs.Screen
+        name="playground"
+        options={{
+          title: 'Playground',
+          tabBarIcon: ({ color, size }) => (
+            <Ionicons name="flask" size={size} color={color} />
+          ),
+        }}
+      />
+    </Tabs>
+  );
+}