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/db/queries.ts

@@ -74,6 +74,48 @@ export function useActivityCount(searchQuery = ''): number {
 
 export { PAGE_SIZE };
 
+export type ActivityFilter = {
+  sport: string;    // '' = all sports
+  dateFrom: string; // '' = no lower bound; ISO-like 'YYYY-MM-DDTHHMMSSZ' for comparison
+  sort: 'date' | 'distance' | 'elevation';
+};
+
+const SORT_SQL: Record<string, string> = {
+  date:      "json_extract(detail_json, '$.started_at') DESC",
+  distance:  "json_extract(detail_json, '$.distance_m') DESC",
+  elevation: "json_extract(detail_json, '$.elevation_gain_m') DESC",
+};
+
+export function useFilteredActivities(filter: ActivityFilter, limit = PAGE_SIZE): ActivitySummary[] {
+  const db = useSQLiteContext();
+  const order = SORT_SQL[filter.sort] ?? SORT_SQL.date;
+  return db.getAllSync<ActivitySummary>(`
+    SELECT
+      id, origin, synced_at,
+      json_extract(detail_json, '$.title')            AS title,
+      json_extract(detail_json, '$.sport')            AS sport,
+      json_extract(detail_json, '$.started_at')       AS started_at,
+      json_extract(detail_json, '$.distance_m')       AS distance_m,
+      json_extract(detail_json, '$.duration_s')       AS duration_s,
+      json_extract(detail_json, '$.elevation_gain_m') AS elevation_gain_m
+    FROM activities
+    WHERE (? = '' OR json_extract(detail_json, '$.sport') = ?)
+      AND (? = '' OR json_extract(detail_json, '$.started_at') >= ?)
+    ORDER BY ${order}
+    LIMIT ?
+  `, [filter.sport, filter.sport, filter.dateFrom, filter.dateFrom, limit]);
+}
+
+export function useFilteredCount(filter: ActivityFilter): number {
+  const db = useSQLiteContext();
+  const row = db.getFirstSync<{ n: number }>(`
+    SELECT COUNT(*) as n FROM activities
+    WHERE (? = '' OR json_extract(detail_json, '$.sport') = ?)
+      AND (? = '' OR json_extract(detail_json, '$.started_at') >= ?)
+  `, [filter.sport, filter.sport, filter.dateFrom, filter.dateFrom]);
+  return row?.n ?? 0;
+}
+
 export function useActivity(id: string): ActivityRow | null {
   const db = useSQLiteContext();
   return db.getFirstSync<ActivityRow>(