Comment 4 for bug 2020264

The dpkg terminal log shows:

Unpacking mariadb-client-core-10.6 (1:10.6.12-0ubuntu0.22.04.1) ...
Setting up mysql-common (5.8+1.0.8) ...
update-alternatives: using /etc/mysql/my.cnf.fallback to provide /etc/mysql/my.cnf (my.cnf) in auto mode
Setting up mariadb-common (1:10.6.12-0ubuntu0.22.04.1) ...
update-alternatives: error: alternative path /etc/mysql/mariadb.cnf doesn't exist
dpkg: error processing package mariadb-common (--configure):
 installed mariadb-common package post-installation script subprocess returned error exit status 2

Note '/etc/mysql/mariadb.cnf doesn't exist'

Seems you deleted of heavily customized folders or files in /etc/mysql which caused this. Steps to recover depends on what update-alternative steps you have currently in effect and what 'find /etc/mysql -ls' shows now as the file and directory structure.