Setting a configInternal setting in AfterInstall

[BattleMetalChris]

I'm trying to set the 'databaseHandler' field of the logger to true in config-internal, using AfterInstall.php in my extension scripts

I'm currently doing

$injectableFactory = $this->container->get('injectableFactory');
$configWriter = $injectableFactory->create(Config\ConfigWriter::class);

$configWriter->set('logger.databaseHandler', true);
$configWriter->save(); 

But all that does is create a field called 'logger.databaseHandler' => true in the main config.php

How do I write to config-internal and set the field inside the existing 'logger' entry?