This can be a real "your mileage may vary" kind of question, I've never seen anything EXACTLY like "Shadows House", and I'm mostly coming at the question as someone who sees the animes first, then reads the mangas if I like what I see, but some that seemed roughly similar to me, mostly in terms of some dark storytelling, mystery-solving, interesting story-telling, similar genre, and/or character development:
- "The Promised Neverland" - I've seen more than one comparison between this one and "Shadows House", and the similarities are obvious: a cast of children with no clear past, living in a house of dark secrets where nothing is what it seems to be, in a gothic horror story. The children in both stories are written as being above-average in intelligence, faced with puzzles that you're invited to work out with them to figure out what's really going on, and how to stop it. The similarities mostly end there and I'm not anywhere near as attached to the cast of characters, but I still find both stories enjoyable.
- "Yokohama Kaidashi Kikou" (AKA "Yokohama Shopping Trip Log") - One of those very odd, gently-paced "iyashikei"/"comforting/healing" variations on the slice-of-life/cute-girls-doing-cute-things genre, about a "robot girl" working in a cafe in a small town on the edge of an unnamed apocalyptic end of the world. A LOT is left to the imagination between the lines in this one, with a lot more going on between the lines for us to put together if we want to, than actually happens on-screen. In keeping with the genre, there's not really a story per se as much as there is a sort of sandbox world where life happens at its own pace and the characters just live their day-to-day lives through it all, but I found the cast of characters really charming in this one, and definitely cared about who the are and what happens to them.
- "Girls' Last Tour" - Follows two orphaned girls, a no-nonsense bookworm and her rowdy sidekick, touring a post-apocalyptic world in an eccentric military surplus vehicle, between looking for their next meal, joking around, and pondering odd philosophical questions. The main characters are incredibly charming and the setting weirdly fascinating and beautiful, so much so that sometimes it's easy to forget just how dark the premise actually is (spoiler: chapters and chapters of story representing months or years of travel through just one city go by without the characters ever seeing a single living creature!), but the world-building is fascinating, and the philosophical storytelling implied through dialogue and symbolism is engaging and interesting.
- "Kino's Journey" AKA "The Beautiful World" - I've not read the manga yet, but the two anime adaptations I've seen are presented in a sort of anthology fable/parable format, following the title character and her talking motor-bike sidekick through a strange world of tiny "countries" (mostly the size of small towns), each run by their own strange - and usually dangrous - set of rules. The storytelling gets pretty dark in some towns and the tone overall is fairly cynical, but I enjoy that sort of thing, and character development isn't really the point (most of the character development is shallow, affecting background characters we only really get to know over the course of a single short story), but I stille found the characters likeable and fun to follow, all the same, and I really enjoyed the weird-town-of-adventure format, allowing for a variety of little self-contained stories.
- "Happy Sugar Life" - An exceptionally dark story about a high-school girl in a world of dark and terrible secrets, who is hiding some horrible secrets of her own, which become much more complicated the moment she falls in love with and "adopts" a little girl. The twisted story reminds me a LOT of something Alfred Hitchcock might have done: I can't say the main characters are especially likeable - it's not that kind of story - but we are definitely running on a backbone of gothic horror with this one, presented through twisted, tongue-in-cheek dark humor. The story really kept me guessing, full of plot twists that went in directions that were too dark for even me to predict: most of the stories above are heartwarming or relaxing in spite of some dark themes and such, but, aside from its ghoulish black humor, this one is definitely not intended to be a feel-good story!
The anime's for the above are worth checking out too, and I'd also suggest these animes (I don't think there are manga versions, and I think they were all made by the same writers, in more or less the same genre):
- "Paranoia Agent" - The story kicks off as a sort of buddy-cop procedural following a cynical older detective and his optimistic rookie partner as they investigate the seemingly random beating of a young cartoonist/character designer, only for them to realize that there is something far stranger and darker at play as a rash of apparent copycat attacks suggest that the whole city - perhaps the entire world - might be in danger. The anime series is presented in a sort of anthology format that tells a different (though connected) sort of horror story about a different character each episode. There's mystery, dark fantasy, horror, black humor, interesting multi-faceted characters with dark secrets, and some brilliant story-telling here, one of my fovorite animes!
- "Paprika" - A movie in which the title character acts as a sort of therapist who helps troubled characters through an invention that allows her to enter their dreams; when a deranged killer steals the device and uses it to commit crimes, the boundaries between dreams and reality begin breaking down, and only Paprika and her friends can stop the madness. Likeable protagonists, a mystery/psychological-thriller format, inventive storytelling, and surreal world-building make this one a stand-out.
- "Perfect Blue" - Another movie, this one about an actress whose role in a very dark crime drama puts her in a great deal of stress, just as she discovers an internet blog dedicated to detailing far more about her life than any casual fan should know, and her coworkers begin getting killed off one-by-one. Is the killer an obsessive fan, a coworker, a ghost, or something far more sinister and terrifying? More likeable protagonists in a mystery/psychological-thriller format, with clever storytelling and surreal visuals - another stand-out.
Again, none of these are exactly like "Shadows House", but I think most will appeal to the same audience in different ways.
