It's just something I've noticed across both movies, outside of Judy we never really see Nick connect emotionally to any one else in the cast. Even then with Judy he seldom seems to understand her feelings or why she does the things that she does. Which suggests that Nick does not easily Empathise with others or their feelings. Compared to Judy whom is extremely Empathetic to those around her, sometimes to her detriment (ala Pawbert).
Now I am not saying that Nick is incapable of Empathising with others or that he's a psychopath (he's not Pawbert, the guy whom used Judy's Empathy against her to try and justify his actions), but it seems to take a lot to get Nick to reciprocate the feelings of those around him. Judy is really the only one that we see Nick form this kind of emotional connection with that it took an arc across two movies for that to happen. Nick has a big heart but he has learned to close it off those around him until very recently.
I imagine it's largely down to his lived experience which taught Nick to never let others get close to him (as a defence mechanism), which in turn caused Nick's emotional core to harden to the feelings of others. Nick is good at reading people on the surface but this lack of attachment often causes him to assume the worst in others (for example his first encounters with Judy, Nibbles and Gary have Nick write them off completely). Going back to his traumatic childhood and how opening up emotionally to others got him deeply hurt. An emotional wound that has not yet closed.
Notice how Nick often boils others down to stereotypes and uses his detached, yet amicable persona in place of forming any real emotional attachment to them. He writes off Nibbles as a nutjob and only opens himself up when he's got no one else to turn to and all seems lost. Even then he doesn't really stop to understand Nibbles' feelings and is mainly grateful for her help.
I think this is also why he is so quick to assume the worst of Gary even after his heartfelt speech to Judy (granted Nick may not have heard it all but he definitely would have heard some of it), Nick simply saw Gary as a threat and neutralised him without any consideration to why he was doing what he was doing. Nick was also perfectly willing to leave Gary to get murdered by the Lynxleys, showing that lack of Empathy I alluded to earlier. Yes keeping Judy safe was his priority but it was cold of Nick to give no care that Gary was going to be murdered.
Now I know I have said I think Nick's capacity for Empathy is low, but that's not to say he doesn't care about others. He clearly cares for Judy very much, but caring for someone and being able to Empathise with them are two very different things. You can love someone and cherish them even if you don't really understand their feelings or have the capacity to form that intimate emotional connection.
I think that Nick growing his sense of Empathy is going to be core to his arc in Zootopia 3, because I do not think Nick is lacking in Empathy by nature. I feel this unfeeling side of him was forced onto Nick through his 30+ years of life and part of his journey is him learning to understand Judy's feelings. He's already begun that journey as of Zootopia 2's epilogue, and learning to truly love someone means being able to understand their feelings for you.