Is it possible to reuse water extracted from the PACKs Water extractors?
Water comes from condensing water vapor present in the cabin, itself coming from human breathing and perspiration, and, for a small part, from atmosphere.

The question mentions an air generation unit which is an Airbus terminology, so let's go into the A380 air system:


A380 Engineering training, source (page 101)

The two green labels are my addition to show the extractor and a spray nozzle. Water separated by a cyclone in the extractor is sprayed into ram air just after the ram air inlet and before entering the heat exchangers of the air-cycle machines. Spraying water droplets creates evaporation, hence a temperature drop in the exchanger receiving fluid, increasing air exchanger capacity.

Bleed air from the engines/atmosphere is colder and dryer at high altitude. Air exchangers work better, but cabin atmosphere may be dry for human well being. A fraction of condensed water can be returned to conditioned air going to the cabin. This is done automatically by the air-conditioning system.

To answer your question: Water is already fully reused.