[Western Crossover] I Took Muzan's Place, Then Ended Up in the Wrong World

Because of a deal with Izanami, a monster from the Abyss spent tens of thousands of years holed up in Hell. Then one day, after tricking a gullible Demon Progenitor, it successfully stole his identity and escaped. But... Why is it daytime in the human world now?! Under the scorching sun, the smoking Muzan sprints across an endless desert, utterly frantic. During his desperate flight, he catches sight of a black lump out of the corner of his eye. Muzan slams on the brakes. Look what he's found! A wild cape! A cape! One that blocks sunlight (underline this)! A cape! Muzan is overjoyed. He quickly snatches it and happily drapes it over himself. At last able to survive under the blazing sun, Muzan breathes a sigh of relief. Thanks for nature's (?) generous gift! What? You say there's someone under the cape too? Well, that's not important ╮(╯▽╰)╭ An injured, unconscious Bat: "..." PS: Also known as The Years I Spent Happily Married to a Bat Cape (?) [Reading Guide] 1. An extremely crack pairing: Batman x Muzan. As the blurb shows, this isn't the original Muzan, and he's a lot more daytime-friendly. 2. This should be a silly comedy to some extent. 3. Muzan's abilities will be buffed somewhat. He's not completely doomed by sunlight. 4. The protagonist doesn't know the superhero world's plot. Theme: Even in another world, you should live well.