But nicotine addiction is physical. Harshal herself, her body, doesn't crave for smoke. It's the body of the war vet that doesn't exist in this world.
Whatever, I don't know how smoking is perceived in Korea so I'll assume it's a Korean thing.
Yes and no, the addiction is indeed physical but there is still going to be a mental component to it too because a person can come to rely on it as their means of relieving stress. It all comes down to why a person smokes. An old soldier that lost limbs on the battlefield is very likely to build an addiction smoking as a means of numbing the pain and any ptsd they might be dealing with. Similarly, the stress of the circumstances he finds himself in would very easily lead him to yearning for his preferred coping mechanism. It's kind of like how depression can lead a person to overeating as a coping mechanism for their emotional state, it's not something your body necessarily craves, but your mind certainly does because it can feel comforting to do so. It's also similar to when many isekai characters yearn for specific foods from their native homeland, such as rice and soy sauce in the case of Japanese characters. Their bodies may not necessarily hold the same experience, but their minds certainly remember such details, and you can very easily expect some level of carry over in that process because of this fact. Now if he had been a smoker that was in the process of trying to quit, then I would very much agree with you since both the body and mind would no longer crave such things, but someone that relied on it is a different story. However, what you said is very likely why he didn't face any issues with withdrawal in Harshal's body, heck, those cigarettes might even be having more of a placebo effect on him when you consider the likelihood of a boss character's body having all sorts of resistances, all that matters is the fact that the one in control of the body THINKS it actually does something for him. Addiction is a twofold thing, and unless a person gets over both the physical and mental/emotional attachments that are generated, they can't be free. This is why it's super important to seek help help from others when trying to curb any addiction because the problem is rarely so simple as getting over the physical aspects of it.