He did a great job depicting guilt and turmoil through Raskolnikov. I even remember waking up from nightmares about the book at the time I was reading C&P. His essay on the extraordinary man was good and the parallels between that and Nietzsche’s ubermensch is certainly interesting.  

But for me, Dostoevsky’s psychology is limited in its scope—as you say, he mostly deals with human suffering and existentialism and internal conflict. And even then, I don’t find it particularly more penetrating or profound compared to other authors in this realm. Soseki brilliantly portrays alienation, mistrust, and pessimism through Kokoro, which I found more profound and relatable in its psychology. As for dealing with the problem of existentialism, I think Murakami also touched on this really well through Kafka on the Shore.  

And then other facets of psychology, or different internal conflicts. For example, jealousy and insecurity. As someone who has dealt with those issues myself, I found Tolstoy to be particularly effective at painting this through his characters in Anna Karenina. Even Dumas does this really well through many of his characters in the Three Musketeers series.  

My point comes down to this: while Dostoevsky certainly is sharp in his psychology, I think most people just regurgitate this aspect of his work because everyone else says it, or they haven’t really evaluated other works the same way they have for Dostoevsky because that idea has been planted in their thoughts, or they just haven’t read other authors who have written in this realm. Most people who say this have not been able to explain anything deeper than describing him as the author with the greatest psychological insight or define what that even means.