There's a very simple reason for this, and it may seem obvious but bear with me: he's only mentioning his fellow crew members, and Carrot, as you said, is not one.
Chopper has most certainly not lost any love for Carrot, that connection didn't just vanish or become unimportant to him. However, it hasn't been talked about for years, and if Oda did have Chopper bring it up now, it would confuse the relatively simple message he's trying to get across, that Chopper's worried about his crewmates.
I still feel like Carrot has been downplayed by Oda with a purpose in mind, which, I get it, is not very convincing. But sticking her in the conversation now would be a huge red flag and is clearly something Oda doesn't want or care to do. Doesn't mean Chopper doesn't care about her, just like he hasn't forsaken Momo, Hyo, Dr. Miyagi or Tristan or any of the Akazaya he also didn't mention.
This kind of thing came up years ago with Jinbe during Fishman Island; he and Luffy were arguing during chapter 634, and Luffy said Jinbe was his tomodachi, his friend, rather than his nakama, his crew mate. That was the very arc Luffy first asked him to join, and the fact that he only considered Jinbe a regular friend up to that point had no negative impact on his final decision.