I am rabidly anti-smoking, but I find their argument, as presented, absurd. To say that your office is a smoke-free workplace and since you are now working from home, your home is the office is outrageous.
Offices have non-smoking policies in their buildings to avoid polluting the indoor air in the workplace, and I'm glad they do. Back in the 1980's I worked in an office that allowed smoking at your desk, and it was awful. The building had poor air quality to begin with, and the cigarette smoke made it much worse.
However, when you work from your own home, the air quality of your home is your call. If you choose to smoke the health consequences are yours to deal with.
Had they said that smoking during video meetings is not allowed it would be a much more honest and legitimate argument. I am a manager, and would complain if any of my people smoked during a video conference because it is now considered unprofessional in the workplace, and projects a bad image. I would talk to the person and frame it that way, and ask the person to refrain from smoking during video meetings in the future. I would never presume to tell them that they could not smoke in their own house however.
(I'm friends with most of my co-workers, and might push on them to stop "driving nails into their coffins" since cigarettes kill a significant portion of their users over the years, but that would be a person-to-person message, not a manager to employee message.)
I don't know if your employer has legal grounds for their position or not. I'd suggest talking to a lawyer before deciding to fight it.
As a new employee, it's probably bestsafest to just respond by apologizing, saying that you were not aware of the rules, and ask for documentation on those rules in order to avoid future accidental violations.