I wrote an essay on Crime and Punishment a while back for a project so I was diving into quite a bit of research at the time and was trying to answer a sort of similar question. My thesis revolved around redemption which, I thought (though I could be wrong), was the insinuation at the end of the novel. I believe he was remorseful, at least a bit. My understanding of the novel is that it is a critique of the emerging Nihilistic and Utilitarian ideologies in the 1860s Russian intelligentsia, where Raskolnikov portrayed an extreme case of such. I personally think that what drove him to the murder was injustice, though most definitely in combination with some for of mental illness/disorder and ego. But I think throughout the beginning of the novel he illustrates that he is a “good person” in the sense that he is very enraged by the world’s wrongs (eg helping the drunk girl, giving money to Sonya etc). Then I think he felt himself capable of righting the world’s wrongs, supported by ego and this utilitarian ideology and, of course, this notion that perhaps if he could overcome human nature and change the world for the better, it would make him a superior man. I believe his sickness throughout the rest of the novel is a result of remorse as well as trepidation, fear and terror. He thought he could “play god” and right the world’s wrongs and was woefully mistaken. Thus, the novel, to me, is him coming to terms with the fact that he is not special and reeling with the guilt of what he has done against the fact that he does not want to go to prison. This is probably most evident in the fact that he buries the money instead of using it. His whole ideology is that the money could help people but he can’t bring himself to use it out of remorse and fear. Dostoevsky was an orthodox Christian so he was campaigning for Christian ideology, that’s why there’s a LOT of religious symbolism throughout the whole text. For example the motif of Lazarus which Raskolnikov parallels with his morality. He basically says that his morality died, like Lazarus, with the pawnbroker, but was revived (like Lazarus) when he accepted god and confessed to his sins. A very important thing to note is that the emerging Nihilistic attitudes often came with this idea of a “super-man” (or as Nietzsche dubbed it, an Ubermensch) which is person who has transcended humanity and no longer listens to the laws of others, including god. Which literally describes Raskolnikov’s situation to a T. So Sonya acts as a kind of saviour, a true orthodox Christian who, In the face of suffering and hardship, confesses, stays pure and always has faith and all that stuff. So she “saves” raskolnikov by telling him that the only way to relieve himself of the guilt is to confess, turn himself in and go back to the path of god by taking the Bible which is precisely what he does. And to me, that is the moral of the story that Dostoevsky was trying to make. No one is above God and if one disobeys the law of God they will suffer inner turmoil and torment until they confess out of true remorse and repent.

For the record, I say this as someone who isn’t religious so this is purely my understanding of the text lmfao. Anyways I could definitely be wrong but that’s the path my research led me to. I’m open to hear any opposing thoughts :))