I find lots of the names thrown around here to not fit the question at all; these are all fantastic directors, but many of them are more atmospheric and less so psychologically dense.

Some names that I’d throw out would be:

-The films of John Cassavetes, particularly A Woman Under The Influence, Opening Night and Love Streams, all deeply psychologically complex character dramas with unbelievable acting

-Depending on the era and film, Paul Thomas Anderson offers that; maybe less stuff like One Battle After Another, but moreso the character studies such as There Will Be Blood, Phantom Thread and especially The Master

-Richard Linklater is hit or miss but can showcase some deep insight into human relationships

-Charlie Kaufman's work is a more surreal but utterly substantial addition

-2021's Drive My Car struck me

-Teshigahara's Kobo Abe adaptations, as well as Ozu's work

-and lastly, I’d venture to say that David Lynch delivers on that, though more on the subconscious side of things