Do not use the system database for tests

Problem/Motivation

All tests are using the system "mysql" database when using MySQL or MariaDB database types. We should use a different one as "mysql" is a system database.

Steps to reproduce

https://git.drupalcode.org/project/drupal/-/blob/11.x/.gitlab-ci/pipelin...
Run any pipeline.

Proposed resolution

Change the name to another one. Not sure if we will need to create it or if the base test classes will create it automatically.

Remaining tasks

MR and tests.