After the System Agreed to Send Me Home, the Villainess Regretted It

Looking for a Story Where the Male Lead Fakes His Death, Returns to the Real World, and the Female Lead Finds Out He's Alive

I'm looking for books like "After Faking His Death, the Sickly Empress Chased Him Into the Modern World". I'd love a story where the male lead enters simulations or transmigrates into a book to complete missions, like simulating life as an empress or a demoness. He fakes his death to fool the heroine, but she discovers he's still alive in another world and transmigrates there to find him.