"Binge" is a word that has become used more frequently in recent times beyond its original context.
The Oxford dictionary defines it as "a period of excessive indulgence in an activity, especially drinking alcohol or eating". So while it doesn't exclusively refer to eating and drinking, that is what it it especially refers to.
For example, the term "binge-watching" has become widely used to describe watching an entire TV series in a short period of time, perhaps even one sitting. This has possibly made the term more widely heard beyond its original use. However it is noteworthy that many dictionaries, including the Oxford, give "binge-watching" its own hyphenated entry rather than just a secondary mention under the root word.
Really, some things do not fit the original meaning of the term "binge". Consider eating. Having regular meals is not considered bingeing. Nor is eating little throughout the entire day - this has its own term "grazing". Binge-eating carries the idea of eating a lot in a short space of time. So with that in mind, can you really binge-watch television? You can't actually watch a show any faster than anybody else. A 45 minute TV show takes 45 minutes to watch, no matter how many episodes you watch back-to-back. I would suggest that the term has been reappropriated for somewhat humourous effect and become a new word in its own right. Likewise smoking has long had its own term for someone who smokes one cigarette after another - "chain smoking". Can you really binge on cigarettes? Unless you can alter the laws of physics and make them burn faster I don't think you can.
But to answer your question about the different uses - I don't think the following example of yours is correct...
She tends to binge on smoking when she is upset.
... because smoking is a also a verb. You wouldn't say:
She tends to binge on eating.
You would say:
She tends to binge on food.
She tends to binge-eat
If you use "binge" as a verb I don't think it sits right with another, unless you hyphenate it or present it as one collective verb like binge-eating or binge-watching. If you are going to use "binge" as a verb in its own right then you need to specify what the person is bingeing on.
Again to make the same point, you would not say:
She binged on watching.
You would say binge-watching, or else specify:
She binged on an entire season of Star Trek Discovery.