Australian here. No one I know would really call anything a "swagman jacket." A swagman was basically the same thing as a hobo in the USA. That is a laborer that travels from place to place.
So any company that wants to sell you Australian themed stuff is probably going to use terms like swagman, jackaroo, stockman, bushman etc.
I think what you're thinking of as a "swagman jacket" is essentially a shortened oilskin duster. A company called "Drizabone" makes that kind of thing so, at least in my circles, those sort of coats would probably be called a "drizabone" like a genericized trademark.
Do we actually wear them? I live in a metropolitan area and mostly the only time I will see them is maybe some people wear them to the Dawn Service, on ANZAC Day, if it's going to rain.
I can't speak to what "real Australians" in the country wear.
