My question is, how do I update PDO to use the latest sqlite3 version?

You have to update the PDO extension, and specifically the sqlite3 driver extension of PDO with the updated libraries.

PDO is part of core, you can find the source code here: https://github.com/php/php-src/?tab=readme-ov-file#building-php-source-code

SQLite3 is already mentioned in the prerequisites before make.