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I think it's a recent thing. I first heard about this analogy some time in the 2010s.

Voltage has been called "pressure" for a very long time, although I'm not sure if it's strictly a hydraulic analogy.

Yep. Traditionally, voltage was the "tension" applied to the system. Pulling rather than pushing there, but same idea. Still occasionally seen in "high tension lines" etc., and for some reason (worked on too many tube amps over the years?) I sometimes still write HT/LT instead of HV/LV.

Where else would you get "voltage sink", "gate" (similarly German "Gatter" - gate, flip flop, switch).

Pretty sure Maxwell used it.

The analogy is just to try to convey the concept of a field and the associated vector calculus. An analogy isn't necessary for Newtonian mechanics and scalar calculus because humans intuitively understand thrown balls etc.

Maxwell's fluids followed EM field lines, not current flow.

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