PDO::ATTR_PERSISTENT => true keeps the MySQL 524 link open when the script ends, so the next request served by the same PHP-FPM worker (Performance and OPcache) skips the handshake. On the test machine that saved little: 0.65 ms for a fresh connection over the local socket against 0.28 ms reused. The costs are larger. PDO does not reset a reused link, so a script that ran SET @cart = 42 left @cart at 42 for the next script on the same CONNECTION_ID(), and temporary tables, open transactions and locks leak the same way. Each worker also pins a connection: 200 FPM children on four servers need 800, against MySQL's default max_connections of 151. Leave persistence off unless you measure a need.
ATTR_TIMEOUT caps the connect attempt in seconds. The server drops links idle for wait_timeout seconds (28,800 by default), and the next query fails with error 2006, "MySQL server has gone away", or 4031. PDO never reconnects by itself, so a long-running worker should catch those codes, open a new connection and retry once, but only outside a transaction, whose work died with the link.