https://www.mangago.zone/read-manga/sangyang_the_wanderer/
not necessarily a detective story but its a mystery that the main character's investigating. the uke's not exactly slutty but he is very flirty with mc. and yes the mc's very mentally unstable (tho tbh they all kinda are).
wait im fucking stupid i didnt see that u wanted smut nvm this story doesn't have any smut its shounen ai sry. ignore what i said (tho i recommend it regardless)
It's okay I'll try to read it looks very interesting tho
Pls recommend me any bl mangas with stories that have detective stories and also hot smut scenes! Bonus if the characters is a slutty uke x mentally unstable seme xD like Memento Scarlet