PHP hasn't been updated? The mysqlnd, if I am correct, is the PHP extension that talks to MySQL.
So, did the actual MySQL database server get updated?
You may need to get your hosting provider to work on this.
See:
https://www.cadence-labs.com/2017/08/wordpress-magento-mysql-php-fix-server-requested-authentication-method-unknown-client/
https://www.eschrade.com/page/the-server-requested-authentication-method-unknown-to-the-client-mysql_old_password/
https://serverfault.com/questions/295285/mysql-cannot-connect-via-localhost-only-127-0-0-1/297310#297310