I learnt about prepared statements when making a JDBC-enabled Java application, and my app uses a connection pooling layer that assures me that prepared statements are cache
If your PHP application uses connection pooling to the database, and the database caches prepared statements, then yes, the caching will persist between pages. If the prepared statement caching is done by the client library, then this is more nebulous.
You need to look at the docs for PHP-FPM and/or PDO to see how to tell them to use connection pooling. There should be an option in both to do it.
You should be aware that MySQL connection setup and teardown is actually very fast and many PHP installations do not use connection pooling because of this. Either way, you should also invest time in your server settings, particularly the wait_timeout parameter. PHP is also designed around the idea that you create everything you need when your pages starts and it all goes away when the page finishes. Most PHP code and libraries assume this is the case. It is quite a different paradigm than under Java.