The entrance to this area is on the east side of the mountain.
There is only one way to get into the Biofoundry... participate in the raid to kill Volan. Once he is defeated you have 120 minutes until the Karthan Core recharges and kicks everyone out of the area. Carnage quests here can be done by anyone at any level, but the questgivers require level 60 before they will talk to you. This includes the final series of Story quests in The Biofoundry.
All Carnage quests in The Biofoundry are repeatable and do NOT count towards Ashora completion achievements. As far as we know, they are the only Carnage quests in Storm Legion that are repeatable.