Where is the Deeper and Darker act?

It opens from The Otherside, a quest in Act II that asks for a Heart of the Deep. Its reward is a button into Act III-b – Deeper and Darker, which the quest book titles “Act III - Deeper and Darker”.

The Otherside needs The Warden and the Dark Iron Ingot quests first, and the Heart of the Deep’s recipe uses a Withered Demon Heart from the Decaying King in the Nether, so in practice the act opens during Act III. It is optional: nothing in the main line depends on it. See The Otherside.