Lin Xun had learned a great deal of intelligence from the Chief Speaker. After returning to Jinling, with his Soul Strength not yet fully restored, he was not in a hurry to enter the Blood Sun World.
One reason was that Omniscience had just harvested a wave of Divinity Fuel and was analyzing the key Authority of the Book of Salvation. The more he could delay entering the chapter, the better.
It would be best to wait until Omniscience had finished analyzing, equipped with the ability to unlock the shackles on him at any time. Then, Lin Xun would not have to worry about being backstabbed by the Administrators after entering the chapter.
The second reason was that the Extreme Delusional Evil Fruit had been destroyed, and it would need sufficient time to grow stronger. Since the Administrators were worried about it growing stronger and gradually becoming uncontrollable, it wouldn't hurt to delay a bit longer.