I'd say here it's a catch-all for something not alcoholic ("hard liquor", not that we'd ever use that term) or any 'brew' (tea/coffee, maybe also hot chocolate/cocoa, notthing to do with alcoholic brewing unless Irish Coffee/with a tot of rum/etc) or an actual juice* (fresh or manufacturer-reconstituted).
By ubiquity - "soft drink" probably now mostly refer to fizzy pops (carbonated soft drinks, in full but rare usage) but also to the diluted cordials (e.g. orange squash) that it originally referred to, before lemonades (not the US-type famously front-yard-trestle-table-fundraising stuff, home-made sugared-water-with-real-lemons-infusing-inna-jug-with-optional-ice, but the carbonated clear citric 'industrial' stuff), orangades, colas, etc came into play and dominated the catering market with the ease of the cans or handy-sized plastic bottles, no mixing required.
But it used to be so simpler, just from lack of option. Soft Drink or Hot Drink or (where served) Beer. Which was likely to be "a pint of best" (bitter, served at ambient temperature), not any lager.(probably also at ambient temperature, hence why often likened to horse-piss).
* - Or maybe it does include juices, but only because of the current continuum of sparkling and non-sparkling waters running through the full gammut to unadulterated and not-from-concentrate juices via all kinds of flavoured-(fizzy-)water intermediaries like your Britviks and J2Os...