I headcannon that Integra didn’t smoke as heavily before the cannon events in Hellsing. The reason why she we see her smoke so much is due to stress she feels from the alarming rates of vampire attacks in England and then the string of events that follow afterwards (aka everything we see in the OVA basically). Before she was actually fairly good at finishing cigars too, the habit of starting new ones and putting out after a puff or two is new.
I can get behind this headcanon. It makes sense that her increased smoking is correlated with stress because everything ramps up to 10, where the OVA starts. I'm not a smoker, but after one too many breaks with coworkers that do smoke, I can say that someone that truly smokes heavily is gonna finish their cigarette (or cigar in integra's case).
