In a configuration form use $this->config() and not \Drupal::config().
The difference between both is that the configuration form uses immutable configuration.
When Drupal 8 was in beta, the immutable configuration was introduced to avoid bleeding of overridden values into configuration when saved to the database. See the change record:
Configuration objects by default are immutable
This is the code executed by $this->config() of a configuration form, in a static version:
\Drupal::configFactory()->getEditable('system.site')->set('name', 'My fantastic site')->save();
For Drupal 8.7 it is discussed to display a warning for overridden values:
This form contains values that have been overridden. Changes to these values can still be saved, but the overridden values will take precedence. Overrides are as follows ...
See the issue:
There is no indication on configuration forms if there are overridden values