From personal interpretation, Yuji has always been a character who would put the lives of others before his own. He knew the risk of swallowing Sukuna's finger and did it anyway. He saved Megumi, then went on agreeing to carry the burden of Sukuna to ensure no one else got harmed. He could have floundered at the moment and curse the world, begging to be spared, but he doesn't. I admire that about him.
During the detention center arc, we see his determination to die his own way get tested, as he's put in a situation where he was about to die if Sukuna didn't step in. He then had to take his own life to save Megumi, again, dying prematurely to the fate he'd accepted for himself. This launches him into working harder to get stronger to ensure that he has some level of control over his death.
But during Shibuya... he loses that control again. He loses control over Sukuna, and comes to realize that he isn't powerful nor is it power that will define the control he has over himself or everyone else. Gojo is the strongest but he got sealed and people still died. Yuji is quite powerful, especially physically, but his friends keep dropping around him. He can't save everyone. Saving people can't be his goal anymore, it's fruitless as people will keep dying, so he needs to focus on killing curses. Focus on the cause of the problem. He's good for destruction, so let him destroy the things he hates the most.
Beyond that, if we go into manga territory, Yuji hasn't lost the spark to care. We see it when Megumi asks Yuji to save him, thus pulling him a bit out of his emotional rut. He's still self-sacrificial, as we can see when Yuji was more than willing to be killed by angel to free Gojo. And Yuji hasn't lost his will to help others as he tries to save those being attacked in the later half of the culling games, and vows to save Megumi again from Sukuna. I think this truly is an embodiment of his grandfather's dying words. Paraphrasing, but the idea of helping people, even if it's just one, ie. Megumi. And when it comes to Sukuna, Yuji was originally determined to take them both out with his execution. Now it seems Yuji is playing executioner or will have to reign the curse in, and whatever he's done during the time skip is in service to that. Sukuna was his original burden, it only makes sense that Yuji would do his damndest to see his fate through to the end.

I think the above thoughts came out a little messy, but all in all, watching this optimistic, hopeful, yet self-sacrificial character become someone willing to do anything to save others while also learning the desire to stay alive until his goal is complete. He continues to fight and get stronger to carry out his desires, and if he didn't have that drive to kill Sukuna and save Megumi, he would have given up a long time ago. The problem is that he still doesn't value is own life outside of what he can do with it in relation to others. He doesn't live for himself or see a future beyond this battle. That's heartbreaking to me.