Initialize Expo mobile app with tab navigation and monorepo support

- Expo managed project at apps/mobile/ with TypeScript
- Expo Router with 4 tabs: Map, Routes, Activities, Profile
- app.config.ts with monorepo experiment, bundle IDs, scheme
- Workspace packages linked: api, gpx, i18n, map-core, types
- Profile tab imports API_VERSION from @trails-cool/api to verify
  shared package resolution

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/mobile/app/(tabs)/_layout.tsx

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+import { Tabs } from "expo-router";
+
+export default function TabLayout() {
+  return (
+    <Tabs
+      screenOptions={{
+        tabBarActiveTintColor: "#4A6B40",
+        headerShown: false,
+      }}
+    >
+      <Tabs.Screen
+        name="index"
+        options={{
+          title: "Map",
+          tabBarIcon: () => null,
+        }}
+      />
+      <Tabs.Screen
+        name="routes"
+        options={{
+          title: "Routes",
+          tabBarIcon: () => null,
+        }}
+      />
+      <Tabs.Screen
+        name="activities"
+        options={{
+          title: "Activities",
+          tabBarIcon: () => null,
+        }}
+      />
+      <Tabs.Screen
+        name="profile"
+        options={{
+          title: "Profile",
+          tabBarIcon: () => null,
+        }}
+      />
+    </Tabs>
+  );
+}

apps/mobile/app/(tabs)/activities.tsx

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+import { View, Text, StyleSheet } from "react-native";
+
+export default function ActivitiesScreen() {
+  return (
+    <View style={styles.container}>
+      <Text style={styles.text}>Activities</Text>
+    </View>
+  );
+}
+
+const styles = StyleSheet.create({
+  container: { flex: 1, justifyContent: "center", alignItems: "center" },
+  text: { fontSize: 18, color: "#666" },
+});

apps/mobile/app/(tabs)/index.tsx

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+import { View, Text, StyleSheet } from "react-native";
+
+export default function MapScreen() {
+  return (
+    <View style={styles.container}>
+      <Text style={styles.text}>Map</Text>
+    </View>
+  );
+}
+
+const styles = StyleSheet.create({
+  container: { flex: 1, justifyContent: "center", alignItems: "center" },
+  text: { fontSize: 18, color: "#666" },
+});

apps/mobile/app/(tabs)/profile.tsx

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+import { View, Text, StyleSheet } from "react-native";
+import { API_VERSION } from "@trails-cool/api";
+
+export default function ProfileScreen() {
+  return (
+    <View style={styles.container}>
+      <Text style={styles.text}>Profile</Text>
+      <Text style={styles.version}>API v{API_VERSION}</Text>
+    </View>
+  );
+}
+
+const styles = StyleSheet.create({
+  container: { flex: 1, justifyContent: "center", alignItems: "center" },
+  text: { fontSize: 18, color: "#666" },
+  version: { fontSize: 12, color: "#999", marginTop: 8 },
+});

apps/mobile/app/(tabs)/routes.tsx

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+import { View, Text, StyleSheet } from "react-native";
+
+export default function RoutesScreen() {
+  return (
+    <View style={styles.container}>
+      <Text style={styles.text}>Routes</Text>
+    </View>
+  );
+}
+
+const styles = StyleSheet.create({
+  container: { flex: 1, justifyContent: "center", alignItems: "center" },
+  text: { fontSize: 18, color: "#666" },
+});

apps/mobile/app/_layout.tsx

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+import { Stack } from "expo-router";
+
+export default function RootLayout() {
+  return <Stack screenOptions={{ headerShown: false }} />;
+}