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It depends on the scope of work done. Many wineries are small, privatly owned businesses and most work there is done by hand as you wrote. These wineries imho are definitely not industrial, but craft. The wines they produce are often sold at their premises or in specialized wine shops. Good restaurants often buy their wines from these wineries.

On the other hand there are also companies doing large scale wine production (and may also produce other alcoholic drinks). Most of the production process in these companies is industrial style, like using huge steel tanks for storage, fermenting and aging and automated production lines for bottling etc. They produce millions of litres of wine annually mainly for supermarkets and multiple shop chains. These I would tag as landuse=industrial + man_made=works + product=wine.

I do not know if there are different terms for these diffenrent types of wineries in english but in german we call the craft wineries “Winzerei” and the industrial ones “Großkellerei”.