Thanks to help from an unlikely source, you can proceed onward to the Qitana Ravel.

Requirements

This quest is available if you have completed the quest In Good Faith.

Starting the Quest

Talk to Almet in the Rak'tika Greatwood to begin the quest. There will be a cutscene.

Search the Destination

Go northeast down the stairs and go east from the wooden platform to the tree root. Go northeast down the tree root, then go southeast along the path of blue flowers. Go northeast when the path of flowers changes direction, and continue going northeast to where the orange arrow is pointing in the minimap. Check on the sparkling Qitana Ravel Entrance to proceed.

The Qitana Ravel

Use the Duty Finder or Duty Support to enter The Qitana Ravel. Please see The Qitana Ravel Guide for a walkthrough.

After you complete the duty in the Qitana Ravel and exit the area, there will be a cutscene. This one is important, so it is recommended to watch it either now or via the Unending Journey in an inn room.

Speak with Y'shtola

Talk to Y'shtola to complete the quest.

Unlock Flying in The Rak'tika Greatwood

"The Burden of Knowledge" is the final quest for unlocking Aether Currents in the Rak'tika Greatwood. If you have completed the other Aether Current quests and attuned to the Aether Currents in the field in this area (which you can find using the Aether Compass in Main Menu > Duty > Collection in this area) you will be able to fly in the Rak'tika Greatwood.

Next Main Scenario Quest

After you complete the quest, talk to Y'shtola to accept the next quest: Bearing with It.