I think it's OI, the FMC gets adopted by the duke, he's black haired and the moma is red haired. They have a daughter with red hair too. Daughter isn't close with the duke, and is trying to be perfect as an heir. Daughter and FMC become close, FMC dyes her hair rainbow by accident because ML is a lil shit. He's also supposed to be the villain, and is an ousted prince.
Can be manhwa, manhua or manga (●'◡'●)ノ
similar to the comment above me,
story is a guy gets isekai’d into an otome game
https://www.mangago.me/read-manga/isekai_tensei_ore_ga_otome_ge_de_kyuuseishu/
It's about a girl that can cure diseases with her blood, a noble that took care of her and used her blood and shit to rise in power, and then another guy with supernatural powers help her leave her shitty life. Supernatural dude is also murderous asf and apparently has an untold past with our girl.
Pretty sure it’s this one: https://www.mangago.me/read-manga/heeran_love_song/