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

includes/query/class-tmdo-post-query-router.php

@@ -27,6 +27,11 @@
  * post_date and skips GROUP BY (one row per post), so MySQL can walk
  * `idx_post_status_date` and stop at the LIMIT.
  *
+ * Found rows (O-4): routed searches drop SQL_CALC_FOUND_ROWS (it counts every
+ * match inside the page query); found_posts_query answers from a COUNT of the
+ * same query, kept in the object cache until posts' last_changed moves (core
+ * post saves, and flat writes via TMDO_Hook_Bus).
+ *
  * 🔒 v2.9.x → v2.10.x frozen contract: never touches user entity. Routes
  * only entity_type='post'.
  *
@@ -53,6 +58,12 @@ class TMDO_Post_Query_Router {
 	/** Query var holding the status / date copy route, when one applies. */
 	private const COPY_VAR = 'wpdo_post_copy_route';
 
+	/** Query var holding the COUNT for found_posts_query. */
+	private const COUNT_VAR = 'wpdo_post_count_sql';
+
+	/** Object cache group for found-rows counts. */
+	private const COUNT_CACHE_GROUP = 'tmdo_found_rows';
+
 	/**
 	 * Per-request answer to "are this group's copies usable?".
 	 *
@@ -71,6 +82,8 @@ class TMDO_Post_Query_Router {
 		add_filter( 'posts_where', array( $this, 'posts_where' ), 10, 2 );
 		add_filter( 'posts_groupby', array( $this, 'posts_groupby' ), 10, 2 );
 		add_filter( 'posts_orderby', array( $this, 'posts_orderby' ), 10, 2 );
+		add_filter( 'posts_request', array( $this, 'posts_request' ), 10, 2 );
+		add_filter( 'found_posts_query', array( $this, 'found_posts_query' ), 10, 2 );
 	}
 
 	/**
@@ -272,6 +285,46 @@ class TMDO_Post_Query_Router {
 		return $groupby;
 	}
 
+	/**
+	 * Drop SQL_CALC_FOUND_ROWS from a routed search; keep its COUNT for later.
+	 *
+	 * @param string|null $request Full SELECT.
+	 * @param \WP_Query   $query   Current WP_Query.
+	 * @return string
+	 */
+	public function posts_request( ?string $request, \WP_Query $query ): string {
+		$request = (string) ( $request ?? '' );
+		if ( empty( $query->get( self::QUERY_VAR ) ) || false === strpos( $request, 'SQL_CALC_FOUND_ROWS' ) ) {
+			return $request;
+		}
+		$request = preg_replace( '/\bSQL_CALC_FOUND_ROWS\s+/', '', $request, 1 );
+		$matches = preg_replace( '/\s+LIMIT\s+\d+(\s*,\s*\d+)?\s*$/i', '', $request );
+		$query->set( self::COUNT_VAR, "SELECT COUNT(*) FROM ( {$matches} ) AS tmdo_found" );
+		return $request;
+	}
+
+	/**
+	 * Answer found rows from the cached COUNT of a routed search.
+	 *
+	 * @param string|null $sql   Default 'SELECT FOUND_ROWS()'.
+	 * @param \WP_Query   $query Current WP_Query.
+	 * @return string
+	 */
+	public function found_posts_query( ?string $sql, \WP_Query $query ): string {
+		$count_sql = $query->get( self::COUNT_VAR );
+		if ( empty( $count_sql ) ) {
+			return (string) ( $sql ?? '' );
+		}
+		$key   = md5( $count_sql ) . ':' . wp_cache_get_last_changed( 'posts' );
+		$total = wp_cache_get( $key, self::COUNT_CACHE_GROUP );
+		if ( false === $total ) {
+			global $wpdb;
+			$total = (int) $wpdb->get_var( $count_sql );
+			wp_cache_set( $key, $total, self::COUNT_CACHE_GROUP, HOUR_IN_SECONDS );
+		}
+		return 'SELECT ' . (int) $total;
+	}
+
 	// ─────────────────────────────────────────────────────────────────────────
 	// Helpers
 	// ─────────────────────────────────────────────────────────────────────────