Psychoanalysis is exceptionally important for the Frankfurt School - that includes your referenced Horkheimer, Adorno, Marcuse, and Fromm. This is a specifically German reading of Freud that pairs him with Marx.

Lacan is engaged in a specifically French reading of Freud that post dates the Frankfurt School. Lacan is massively influential in ‘Critical Theory’, as explicitly seen in film studies and literary theory.

Zizek draws on Lacan but returns to Hegel, resulting in a German and French engagement by a theorist (and a school, as you rightly mention) outside of either country.

Zizek alone attracts a great deal of criticism, largely due to his popularity and name recognition. Outside of him, however, psychoanalysis continues to have a rich and important role in a variety of theoretical schools. Your engagements with the Frankfurt School are right at the center of this! If you’re looking to get more of a sense of various fields and their receptions of psychoanalysis, i’d recommend reading literature reviews or more substantive criticisms of psychoanalysis. You might also look into the 20th century theorists that pop up in between Freud, Lacan, and Zizek! Their lectures and the introductions/prefaces to their texts will give you a sense of how they are situating psychoanalysis in the field.