If the gears don't at least require an app with a subscription and regular updates to use, they must be old tech

/sarcasm

You could improve it by making the cylinders have sticky-out bits that would scoosh the fluid around better, like little paddle wheels, and if you wanted to get some serious torque transfer you'd push the two paddle wheels so close together that the paddles actually kind of intersect.

    Well, this car is automatic
    It's systematic
    It's hydromatic
    Why it's greased lightnin' (greased lightnin')

I can see the "passive" cylinder getting dragged around a little by viscosity but I don't see how this could transfer even the tiniest amount of power.

Are you sure?

https://en.wikipedia.org/wiki/Continuously_variable_transmis...:

“The most common type of CVT uses a V-belt which runs between two variable-diameter pulleys.

[…]

A belt-driven design offers approximately 88% efficiency, which, while lower than that of a manual transmission, can be offset by enabling the engine to run at its most efficient speed regardless of the vehicle's speed.

[…]

Disadvantages of a hydrostatic CVT include:

Reduced efficiency. Gears are one of the most efficient methods of mechanical power transmission, with efficiencies as high as 90 percent in many cases. In contrast, few hydrostatic transmission systems achieve more than about 65 percent efficiency”