Before Katy Perry and John Mayer went public with their romance this week, they were inseparable while incognito at “Sleep No More.” Spies say the lovebirds stayed attached at the hip at the show, wandering through the interactive play together at the McKittrick Hotel, where audience members wear spooky white masks. Afterward, they canoodled into the wee hours at the show’s Manderly Bar, spies said. Also seen at “Sleep” this week: Taylor Swift, Dakota Fanning and Vince Vaughn.