The reason for “this highly unusual thing” is the problem regarding Ubuntu described here:
If ‘your’ distribution of choice is RedHat based so be it 
I changed only the host name so far.
These are the values set for the database:
*db_manage: true
*db_type: postgresql
*db_adapter:
*db_host:
*db_port:
*db_database:
*db_username: foreman
*db_password: xxx
*db_sslmode:
*db_root_cert:
*db_pool: 5
*db_manage_rake: true
Maybe my postgres installation is the real problem.
I installed it from scratch. (It is not the version shipped with CentOS!)
The standard (postgres) path is: /var/lib/pgsql/11/data
But the foreman-installer is looking for this path: /var/lib/pgsql/data
So I created a sym link from /var/lib/pgsql/11/data to /var/lib/pgsql/data
But after the installer has run the link is vanished and a real empty directory has been created.
Maybe this line from /var/log/foreman-installer/foreman.log helps:
[DEBUG 2020-04-22T09:34:41 main] Hook /usr/share/foreman-installer/hooks/boot/10-reset_foreman_db.rb returned #<Clamp::Option::Definition:0x000000018c5130 @switches=["--reset-foreman-db"], @type=:flag, @description="Drop foreman database first? You will lose all data! Unfortunately we\ncan't detect a failure at the moment so you should verify the success\nmanually. e.g. dropping can fail when DB is currently in use.", @default_value=false, @multivalued=nil, @attribute_name="reset_foreman_db"> [DEBUG 2020-04-22T09:34:41 main] Hook /usr/share/foreman-installer/hooks/boot/11-detailed_exitcodes.rb returned #<Clamp::Option::Definition:0x000000018cbfa8 @switches=["--detailed-exitcodes"], @type=:flag, @description="Provide transaction information via exit codes, see puppet-agent(8)\nfor full details.", @default_value=false, @multivalued=nil, @attribute_name="detailed_exitcodes">