feat(mobile): search/filter tab — sport, date, sort; hidden on Karoo

Adds a fourth tab visible only on Android API 29+ (full phone, not Karoo).
Filters by sport pill, date preset (7d/30d/6mo/year), and sort order
(newest/distance/elevation). Paginated FlatList with the same activity cards.

ActivityCard extracted to mobile/components/ActivityCard.tsx so both the
feed tab and the new search tab share the same component without duplication.

mobile/app/(tabs)/_layout.tsx

@@ -1,6 +1,9 @@
 import { Tabs } from 'expo-router';
+import { Platform } from 'react-native';
 import { useTheme } from '@/ThemeContext';
 
+const isKaroo = Platform.OS === 'android' && (Platform.Version as number) < 29;
+
 export default function TabLayout() {
   const theme = useTheme();
   return (
@@ -20,6 +23,14 @@ export default function TabLayout() {
         name="import"
         options={{ title: 'Import', tabBarIcon: ({ color }) => <TabIcon label="↑" color={color} /> }}
       />
+      <Tabs.Screen
+        name="search"
+        options={{
+          title: 'Search',
+          tabBarIcon: ({ color }) => <TabIcon label="⌕" color={color} />,
+          href: isKaroo ? null : '/search',
+        }}
+      />
       <Tabs.Screen
         name="settings"
         options={{ title: 'Settings', tabBarIcon: ({ color }) => <TabIcon label="⚙" color={color} /> }}