In 2399, multiple ships of this class were in a fleet led by the USS Zheng He to the planet Coppelius, where they acted as protectors of the synthetic lifeforms living there. (PIC: "Et in Arcadia Ego, Part 2")
Inquiry-class ships featured the saucer section / engineering section / warp nacelle layout common to most Starfleet vessels. The class contained two variations of warp nacelles. (PIC: "Et in Arcadia Ego, Part 2")
The Inquiry class was identified by name by Michael Chabon. He identified the class as "a heavy cruiser: the Inquiry-class. That's the Zheng He." Originally, when asked by fans on his Instagram account, he identified the USS Zheng He as a Curiosity-class ship, but he later amended the classification of the ship.