When I configured the server I used the following command to protect mysql: mysql_secure_installation. If I run it again, it tells me that the root user is already protected by a password.
No need to run that script 
The i-MSCP installer is doing the same job for you...
Well, do you have any /root/.my.cnf file ?
If you cannot figure out alone, give us access to the server. Right now, I cannot reproduce.
I can send you the credentials as a private message.
Sure, then, I'll do the update for you after eating I would want be able to reproduce at least on one server to commit a fix in our development branch if needed;)
Done.
Problem was due to the fact that mariadb-server was removed by i-MSCP installer due to a missing package in distribution packages file. To resume, the MariaDB server (mariadb-server-core-10.1 package) depends on the libmysqlclient18 package but other packages that are provided by Ubuntu Xenial such as libdbd-mysql-perl depends on libmysqlclient20 ...
If you need rerun the i-MSCP installer, do it from the /usr/local/src/imscp-1.4.4/ directory for which the distribution packages file is fixed already.
Thank you.