Plesk installation fails on server with MySQL service: ERROR while trying to establish test connection

Symptoms

Plesk installation fails with the error:

Error message or request description : *****  problem report *****
ERROR while trying to establish test connection. If you are installing Plesk on an already configured MySQL server, you need to specify the administrator's credentials to succeed with the installation. To do this, you need to create a file - /root/.my.cnf with the 'client' section where you need to provide user and its password ("user = $admin_name" and "password = $admin_pass"). After installation is finished, the file /root/.my.cnf will be renamed to /root/.my.cnf.bak
Check the error reason(see log file: /var/log/plesk/install/plesk_12.0.18_installation.log), fix and try again
Synchronizing the Debian APT package index files.

Cause

Mysql had already been installed.

Resolution

Prepare the environment for Plesk installation with pre-installed MySQL/MariaDB server according to How to install Plesk on Linux with specific pre-installed MySQL version?