(I should say I'm a :LIB: and am reading the abridged Julian Borchardt version of Capital, so maybe there's an excised chapter that explains this or maybe there's a later chapter that does - I'm currently reading Decade of the Rate of Profit from Part II, chapters 13-15)
It seems that he insists surplus value is directly related to variable capital (i.e. labour), but other than semantically defining it that way, is this necessarily so? From the capitalist perspective how is labour really any different from any other input?
For instance, if one has a theoretical FALSC-style factory with no labour, surely one could still add surplus value to goods?
Any theory reading is good, not lib! Marx wrote in complicated sentences and often belabored a point until it became confusing. I strongly recommend companion material when reading Marx!
The gist of your larger question is really about the semantics of surplus labor value vs. the value created through both labor and fixed capital, e.g. a printing worker + a printing press. The paper published has added value to the raw materials and other inputs, obviously, and when automation comes along and removes the printer's job entirely, that fact won't change. This doesn't disagree with Marx's categorizations at all, in fact he leverages these facts in order to make his distinctions.
Surplus labor value is not the value produced by labor, it's a subset of it under capitalism: the part for which the laborer was not paid and that the owner keeps for themselves. In a system where automation were complete and nobody had to trade their labor with an owner, there can be no surplus labor value because there is no owner leveraging their capital to pocket the difference.
Capitalism depends on exactly what his relationship to function, it's the whole driving force behind the system: leveraging the accumulated productive assets (the means of production) to deliberately underpay labor so that they can pocket the difference and use it to buy even more capital (and yachts and caviar). In fact, the reason the system could overtake other systems to become dominant, according to Marx, is that it became possible to graduate past primitive accumulation (small-time merchants, etc) is through industrialization, through production advancing to a point where a worker is only involved in one small piece of production rather than creating whole products from inputs to selling. Through that process, the social relations become distinctly capitalist: the workers can only sell their labor, the capitalists can only gain through acquiring more capital and taking as much surplus labor value as possible.
Per Marx, labor is different from other inputs because exploitation, i.e. the reaping of surplus labor value, emerges from a social relation (the owner-worker class antagonism). With fixed capital, you're stuck with the flat rate of whatever it took to buy the widget. With labor, you can leverage social relations to decrease labor cost, specifically through owning capital and eventually having a monopoly on violence, e.g. cops and Pinkertons.