OHHHHH, have you not been speaking with Zessura? She advances the plot forward twice. First by renovating the algae farm chambers (the rooms to the side of the Omni sanctum (the pool room)), then in the private chambers to the bottom right (rebuilding the ruins and unlocking the academy to the top right).
Zessura is in her tent: top right in the ruins. Then moves to the private chambers bottom right of the pool chamber.
Zessura does not advance the plot before certain things happen however, explore the map around a bit, quests often activate when entering certain areas after certain conditions are met.
I'm gonna have to write a game guide sometime in the future, to help people keep track of everything.