Updates to add more ads and fix ad types.

lib/services/db_schema.dart

@@ -48,6 +48,29 @@ const createAdFreeEntitlementTableSql = '''
   )
 ''';
 
+/// A single-row table (`id` is always `1`) holding the earliest-known
+/// moment this app was ever used — see `AppState.firstUsedAt` and
+/// `DatabaseService.getOrCreateFirstUsedAt`. Synced like
+/// `ad_free_entitlement`, for the same reason: without it, reinstalling
+/// would reset the new-user ad grace period every time.
+const createAppUsageTableSql = '''
+  CREATE TABLE app_usage (
+    id INTEGER PRIMARY KEY CHECK (id = 1),
+    first_used_at INTEGER NOT NULL
+  )
+''';
+
+/// Unlike every other merge statement here, this keeps whichever row has
+/// the *smaller* `first_used_at` — merging in a device that's had the app
+/// longer can only push "first use" earlier, never later.
+const mergeAppUsageSql = '''
+  INSERT OR REPLACE INTO main.app_usage (id, first_used_at)
+  SELECT r.id, r.first_used_at
+  FROM remote_db.app_usage r
+  LEFT JOIN main.app_usage l ON l.id = r.id
+  WHERE l.id IS NULL OR r.first_used_at < l.first_used_at
+''';
+
 /// Selects fuel entries whose receipt photo still needs uploading to
 /// Drive. Deliberately requires `receipt_drive_file_id IS NULL`, not just
 /// "has a local path": once a row is uploaded, its local copy may still be