
Here's some more "complex" completed manhwas I've read and liked before:
-At the End of the Road (BL, supernatura)
https://www.mangago.zone/read-manga/geu_kkeute_issneun_geos/
-Save Me ( Psychological, a little depressing..)
https://www.mangago.zone/read-manga/save_me/
-Am Uncomfortable Truth (Tragedy)
https://www.mangago.zone/read-manga/an_uncomfortable_truth/
-My student can't be a psychopath (Psychological, has some funny moments from what I remember)
https://www.mangago.zone/read-manga/my_student_can_t_be_a_psychopath/
-Unknown Code (Like a sci-fi fantasty and mystery story, honestly I don't remember. Its based off of a online game that doesn’t exist anymore )
https://www.mangago.zone/read-manga/unknown_code/
-Murderer Llewellyn's Enchanting Dinner Invitation (BL, another Psychological one...)
https://www.mangago.zone/read-manga/murderer_llewellyn_s_enchanting_dinner_invitation/
-A Painter Behind the Curtain (BL, historical, a rollercoaster of emotions lol)
https://www.mangago.zone/read-manga/a_proxy_painter/
I've never read "Kill the villianess" but maybe
"Taming a Shrew" would be similar or maybe not. Apologize in advance haha
https://www.mangago.zone/read-manga/taming_a_tomboy/

(Hopefully, maybe you'll like these! Warning: some contain dark themes/images)
Kichii!!
Phantom Tales of the Night
Death Note
Sunny (MATSUMOTO Taiyou)
Oyasumi Punpun
Monster
Efforts Never Betray
Three Days of Happiness
Totsukuni no Shoujo (says it's ongoing, but according to MAL, it is completed)
20th Century Boys
Venus in the Blind Spot
any genres, as long as none of the main characters are a Mary sue type of character, complex writing would be nice, like "kill the villainess" or "checkmate" by tan