fix(mobile): clear technical debt — real SHA-256, feed pagination, search

source_hash: BAS JSON import now computes SHA-256 via crypto.subtle.digest
instead of the '${id}-${length}' stub. No extra package — Hermes supports
Web Crypto API natively.

Feed pagination: useActivities(query, limit) accepts a LIMIT parameter.
The feed screen starts at 50, calls loadMore() via FlatList onEndReached
(threshold 0.3) to increment by 50 each time. useActivityCount(query)
drives the hasMore guard so loadMore is a no-op at the end of the list.

Feed search: compact TextInput below the header filters by title via
SQLite json_extract LIKE. Changing the query resets limit to PAGE_SIZE
so stale paginated results don't linger.

Docs: close the three resolved debt items; keep only the accepted
background-polling limitation as a known gap.

mobile/db/queries.ts

@@ -29,10 +29,11 @@ export type ActivitySummary = {
 
 // ── Activities ─────────────────────────────────────────────────────────────
 
-export function useActivities(): ActivitySummary[] {
+const PAGE_SIZE = 50;
+
+export function useActivities(searchQuery = '', limit = PAGE_SIZE): ActivitySummary[] {
   const db = useSQLiteContext();
-  // Summaries are derived from the stored detail_json at query time.
-  // JSON extraction via SQLite's json_extract keeps the table schema simple.
+  const like = `%${searchQuery}%`;
   const rows = db.getAllSync<{
     id: string;
     origin: 'local' | 'remote';
@@ -53,11 +54,26 @@ export function useActivities(): ActivitySummary[] {
       json_extract(detail_json, '$.duration_s')       AS duration_s,
       json_extract(detail_json, '$.elevation_gain_m') AS elevation_gain_m
     FROM activities
+    WHERE (? = '' OR json_extract(detail_json, '$.title') LIKE ?)
     ORDER BY json_extract(detail_json, '$.started_at') DESC
-  `);
+    LIMIT ?
+  `, [searchQuery, like, limit]);
   return rows;
 }
 
+export function useActivityCount(searchQuery = ''): number {
+  const db = useSQLiteContext();
+  const like = `%${searchQuery}%`;
+  const row = db.getFirstSync<{ n: number }>(
+    `SELECT COUNT(*) as n FROM activities
+     WHERE (? = '' OR json_extract(detail_json, '$.title') LIKE ?)`,
+    [searchQuery, like],
+  );
+  return row?.n ?? 0;
+}
+
+export { PAGE_SIZE };
+
 export function useActivity(id: string): ActivityRow | null {
   const db = useSQLiteContext();
   return db.getFirstSync<ActivityRow>(