psychology manga

https://www.mangago.zone/read-manga/brutal_satsujin_kansatsukan_no_kokuhaku/

https://www.mangago.zone/read-manga/dareka_o_norawazu_ni_irarenai_kono_sekai_de/

https://www.mangago.zone/read-manga/efforts_never_betray/

https://www.mangago.zone/read-manga/zankyou/ (ig this one kinda has romance but it's relevant to the plot so...)

https://www.mangago.zone/read-manga/massacre_happy_end/ (again has some romance but it's relevant to the plot)

Carnby's work tho again some have romance

Efforts never betray and carnby's work are manhwas tho

Save Me (korean manhwa) : a psychopathic new student wants to be friend with a disabled student who is a victim of a bully. Very stressful

Dokgo (there's prequel & sequel) : a model student died of suicide and his twin came in school as him to find out who bullied his brother (psychological & action)

Peter Pan (Korean Manhwa) : peter pan literally came to visit victims of bullying and gave punishment to the bullies (really gore and cruel, very psychological)

Have to recommend https://www.mangago.zone/read-manga/liar_game/ which actually got me into psychology

(It's been a while since I've read most of these, but as far as I remember, there's no romance. If there was, it wasn't anything significant. Warning: most of these contain dark themes/images)
From the Red Fog
Venus in the Blind Spot
Sunny (MATSUMOTO Taiyou)
Death Sweeper
When Night Falls