HI Marc!
Yes, It is common problem that Ubuntu (and other Debian derivatives) have mysql as default and it's security is set so that it cannot run database server safe thread if database exists in user's directory (here ~/.config/cqrlog/database)
MariaDB allows that, and that¨s why it is the engine to use with Cqrlog.

You do not tell what is your Cqrlog version. If it is 2.6.0 (compiled from source as there is no package) it has three options at fresh start to choose where store your logs.

1)
to user directory ~/.config/cqrlog/database. That is the default and easiest, if database engine allows that.
Full backup is the easiest possible: just copy whole ~/.config/cqrlog to safe place.

2)
to local machine's default sql server that runs @ port 3306. In this case Cqrlog tries to create SQL user for Cqrlog and give all privileges for it. It also creates backups scripts (mysqldump) for backup of the log database and copy of ~/.config/cqrlog (both needed in this case).

3)
Same as 2) but user have to create the SQL user, backups scripts and set values to "Database connection" window by himself. For advanced users. (This is same as uncheck "Do you want to save log data to local machine" at frist start of older Cqrlog versions).

If you have many databases running I assume you are familiar with mysql and can create Cqrlog database user and backup scrips by yourself.

To get a new fresh start, IF YOU HAVE NO LOGS YET IN ~/.config/cqrlog/database, you need just delete folder ~/.config/cqrlog It cleans ALL logs and SETTINGS and gives fresh, first time start for Cqlog again.

Once done that make Cqrlog SQL user before starting Cqrlog.

sudo mysql

When you get mysql prompt type following lines (copy /paste):

CREATE USER IF NOT EXISTS 'cqrlog'@'localhost' IDENTIFIED BY 'cqrlog';
GRANT ALL PRIVILEGES ON *.* TO 'cqrlog'@'localhost';
FLUSH PRIVILEGES;
QUIT;

You may have to change localhost to IP address of your SQL server network card's address if your SQL server runs at different machine than Cqrlog.
You can also alter GRANT to give all privileges just for cqr%.* instead of *.* to get little more security (all cqrlog databases begin with "cqrlog")

Then start Cqrlog.
Be sure NOT to select "save log data to local machine". Then you will see columns for SQL user and password and SQL server IP address and port. Fill them and check "remember" and "auto connect"
Click "connect" and creation of first log should begin.

I have used SQL server at localhost, 3306 since the beginning of Cqrlog usage and it has worked perfectly. Also from remote network address (via ssh and Openvpn tunnels).
I also have database replication with ham computer's sql-server and my home server's sql-server for keeping databases in two places.