Fatal error when installing website from existing config and dblog is not enabled

Problem/Motivation

When installing a website in the web UI, and using existing configuration, if in the existing configuration Dblog is uninstalled, then there is a fatal error:

The website encountered an unexpected error. Please try again later.
Drupal\Core\Database\DatabaseExceptionWrapper: SQLSTATE[42S02]: Base table or view not found: 1146 Table 'drupal.watchdog' doesn't exist: INSERT INTO "watchdog" ("uid", "type", "message", "variables", "severity", "link", "location", "referer", "hostname", "timestamp") VALUES (:db_insert_placeholder_0, :db_insert_placeholder_1, :db_insert_placeholder_2, :db_insert_placeholder_3, :db_insert_placeholder_4, :db_insert_placeholder_5, :db_insert_placeholder_6, :db_insert_placeholder_7, :db_insert_placeholder_8, :db_insert_placeholder_9); Array ( [:db_insert_placeholder_0] => 0 [:db_insert_placeholder_1] => cron [:db_insert_placeholder_2] => Starting execution of @module_cron(). [:db_insert_placeholder_3] => a:1:{s:7:"@module";s:7:"comment";} [:db_insert_placeholder_4] => 6 [:db_insert_placeholder_5] => [:db_insert_placeholder_6] => https://web.docker.localhost/core/install.php/?existing_config=1&langcode=en&profile=minimal&rewrite=ok [:db_insert_placeholder_7] => https://web.docker.localhost/core/install.php?rewrite=ok&langcode=en&existing_config=1&profile=minimal [:db_insert_placeholder_8] => ::1 [:db_insert_placeholder_9] => 1664968020 ) in Drupal\dblog\Logger\DbLog->log() (line 78 of core/modules/dblog/src/Logger/DbLog.php).
Drupal\dblog\Logger\DbLog->log(6, 'Starting execution of @module_cron().', Array) (Line: 103)
Drupal\dblog\Logger\DbLog->log(6, 'Starting execution of @module_cron().', Array) (Line: 127)
Drupal\Core\Logger\LoggerChannel->log(6, 'Starting execution of @module_cron().', Array) (Line: 114)
Drupal\Core\Logger\LoggerChannel->info('Starting execution of @module_cron().', Array) (Line: 235)
Drupal\Core\Cron->Drupal\Core\{closure}(Object, 'comment') (Line: 405)
Drupal\Core\Extension\ModuleHandler->invokeAllWith('cron', Object) (Line: 257)
Drupal\Core\Cron->invokeCronHandlers() (Line: 136)
Drupal\Core\Cron->run() (Line: 75)
Drupal\Core\ProxyClass\Cron->run() (Line: 1871)
install_finished(Array) (Line: 700)
install_run_task(Array, Array) (Line: 571)
install_run_tasks(Array, NULL) (Line: 119)
install_drupal(Object) (Line: 48)
require('/project/app/core/install.php') (Line: 4)

While there is no error when reinstalling using Drush.

Steps to reproduce

1. Install a website using the minimal profile
2. Uninstall the Dblog module
3. Export the configuration
4. Drop the database
5. Install the website using web interface
6. Select "use existing config"
7. On the last stage, after entering maintenance compte credentials, you obtain the error in screenshot

Obtained on Core 9.4.7.

Proposed resolution

Be able to install a website from existing config and without Dblog.

Remaining tasks

1. Identify why the dblog logger service is detected during the installation of a profile without dblog
2. provide a fix

User interface changes

None

API changes

None

Data model changes

None

Release notes snippet

Should not be needed.