I am happy to close my question as solved.
The absent of mysql.sock was not a problem — it is being created during the server startup, automatically.
The obstacle was /var/db/mysql/my.cnf. I didn’t suspect that because its content is right — the same as in /usr/local/etc/mysql/my.cnf. Apparently this file was copied here by Webmin I allowed to start first. Weird, MariaDB refuses to start with this correct my.cnf.
MariaDB server started and Webmin recognized to manage it only after removing my.cnf from /var/db/mysql/.
Cheers!