On the other hand, the quantization of energy states into discrete levels as opposed to a continuum is exactly why the phrase "quantum leap" implies a sudden, very noticeable, step-change jump in some quantity.

AFAIK that usage traces back to the 1990s TV show "Quantum Leap", in which the protagonist would travel in space & time to a new place each episode.

The phrase 'Quantum Leap', then, was popularly taken to mean a large change.

The damage done to the vernacular by that show's title is only exceeded by the damage done to the vernacular by another piece of 1990s popular culture, Alanis Morissette's song 'Ironic'.

The common expression would be "a quantum leap". Which has nothing to do with the "size" of a quantum, but suggests a massive (technological) improvement and increase in capabilities - like going from a normal binary computer to a quantum computer.