The DatabaseSchemaUpdater is called during runs of the update.php script.
This might be a somewhat more complex task as the two classes ItemTermsRebuilder and PropertyTermsRebuilder might need some refactoring to get rid of "unusual" calls like:
$this->loadBalancerFactory->rollbackMasterChanges( __METHOD__ );
See T283330 for thoughts on how to refactor these classes.
Changing ILBFactory in PropertyInfoTable is not part of this ticket as that class is very integrated in a lot of places and thus done as a task of its own: T283343.