What made tobacco use so much more noticeably lethal was that at some point in the 19th century, it became more common to inhale the smoke. This is directly associated with the increasing popularity of the cigarette starting in the late 19th century.
It was also known since the mid-19th century at the very least that tobacco use in any sort was bad for you. It's just it was wrapped up in the pseudoscience of Victorian moralism, hence the specific warnings given to women in anti-smoking pamphlets and such. There were also many products marketed in the 19th century to try and get people to quit, which predictably involved lots and lots of pseudoscience.
But was the state of medicine in the 19th century even conducive to determining things like this? The risks of asbestos wasn't known until the very end of the century, after all. And I don't even think that having science on your side would do much when the tobacco industry can just say "how do we know it's tobacco that causes these diseases and not polluted cities, workplaces, or homes or the person that causes this?" Yes, that's what they did in the 1950s onward, but it seems like a viable strategy to use regardless, and I doubt that science can produce papers as authoritative they did in the 1950s in, say, the 1850s or even 1890s.
So you're gonna need a straight up legal ban. Some Prohibitionists targetted tobacco use, and after Prohibition succeeded, parts of the movement targetted tobacco and actually succeeded at getting local and state bans passed that were poorly enforced. But if there's greater scientific evidence that's publically much more well known in the late 19th century, then tobacco prohibition could latch onto alcohol prohibition. However, this would give Prohibition powerful enemies in tobacco-growing states, so this could easily weaken the movement and ensure that there wouldn't be Prohibition of either alcohol or tobacco at the national level.
Associating it with moral panics is what would help fuel tobacco prohibition. Any anti-smoking movement is going to probably look like Nazi Germany's anti-smoking campaign, which goes back to the issues of the times--it's going to have lots of good ideas and factual science in it mixed with utter nonsense, including healthy doses of racism and old-school sexism.
Now why I wrote this is because the OP speaks about the harms of tabaco. For a person of the 18th/19th century to get the same sintomes as a modern smoker he would had to smoke in very very large quantities. So if they do the connection, and basing themselves on what they know, they will just conclud that heavy smoking is harmful, but that light smoking isn't, which we now know ain't true.
Now this could be the beginning of a period of adjustment in which people will get more interested in the effects of tabaco.
This is true, and it was of course well-known that heavy smoking was bad for you, if only under principles like "anything in excess is bad" and such.
I've talked to people born in the late 1950s and early 1960s and they have no memory of not knowing.
Not knowing what? Everyone
heard about it, but it wasn't until the 1980s onward that public knowledge actually caught up. Public polling shows that significant amounts of people simply didn't believe it was an issue (in particular before the Surgeon General's report), leading to the conclusion that "it isn't a proven scientific fact that smoking causes lung cancer, so let's smoke anyway". Or put it this way, everyone in America knows that science says that humans are the primary cause of climate change, whether they chose to believe that and thus make decisions based on that knowledge, well, that's something else.