perf(2meet-data-optimizer): cache found-rows counts for routed queries

- TMDO_Post_Query_Router drops SQL_CALC_FOUND_ROWS from routed searches
  (posts_request) and answers found_posts_query from a COUNT(*) of the
  same query, cached in the object cache under posts' last_changed.
- Hook Bus flat post writes and deletes move posts' last_changed: in
  aeav_only they skip update_metadata()'s own hooks, so query caches
  would otherwise outlive the write.
- Bench (1M): cached page 8 ms (was 694 / 363 ms for scenarios 1 / 2);
  after invalidation 8 ms + COUNT 608 / 344 ms, on par with before.
- REST X-WP-Total COUNT is on the frozen Hot zone path (ADR-003): not
  changed.
- Verify: core unit 659 / integration 475, HP 142/49, WC 10/22 green,
  phpcs clean
- PR: PR-030

includes/engine/class-tmdo-hook-bus.php

@@ -346,6 +346,7 @@ final class TMDO_Hook_Bus {
 
 			// 清除快取
 			TMDO_Cache_Orchestrator::invalidate( $type, $entity_id, $group );
+			self::touch_posts_last_changed( $type );
 
 			// 短路回傳 true（WP 認為寫入成功）
 			return $result !== false;
@@ -574,6 +575,8 @@ final class TMDO_Hook_Bus {
 			TMDO_Cache_Orchestrator::invalidate( $type, (int) $object_id, $group );
 		}
 
+		self::touch_posts_last_changed( $type );
+
 		do_action( 'wpdo_after_delete', $type, (int) $object_id, $meta_key, $meta_value, $result, (bool) $delete_all, $before_value );
 
 		// 若還要寫 EAV → return null 讓 WP 繼續刪除原生 meta
@@ -613,6 +616,20 @@ final class TMDO_Hook_Bus {
 	// 工具方法
 	// ─────────────────────────────────────────────────────────
 
+	/**
+	 * Flat post writes skip update_metadata()'s own hooks in aeav_only, so
+	 * move posts' last_changed here: caches keyed on it (WP query caches,
+	 * routed found-rows counts) must not outlive the write.
+	 *
+	 * @param string $type Entity type.
+	 * @return void
+	 */
+	private static function touch_posts_last_changed( string $type ): void {
+		if ( 'post' === $type ) {
+			wp_cache_set_posts_last_changed();
+		}
+	}
+
 	/**
 	 * 從當前 filter 名稱推斷實體類型
 	 * 例：update_user_metadata → user