SpecialUnconnectedPages uses the LoadBalance in methods that it inherits from the abstract core class QueryPage:

$this->setDBLoadBalancer( $loadBalancer );

$dbr = $this->getDBLoadBalancer()->getConnectionRef( ILoadBalancer::DB_REPLICA );

We still want to use the DomainDb abstraction here, but after confirming with @Addshore, it seems this is one case where we probably have to use the deprecated \Wikibase\Lib\Rdbms\DomainDb::loadBalancer() method.

The idea would probably to use DomainDb::loadBalancer() with \QueryPage::setDBLoadBalancer() in the constructor, but to then also store the DomainDb in a private field and use it instead of the \QueryPage::getDBLoadBalancer() method when getting the connection.