Are internal focusing primes actually uncompensated varifocal lenses?

If I shorten the focal length of a lens without taking any other measures, that will reduce the required flange distance for infinity focus – meaning that if the actual flange distance is not changed, the focus will be closer than infinity.

Is this effect used to achieve internal focus on prime lenses, and does it explain the effective focal length decreasing instead of increasing in such designs when focused closer?

In other words, do such lenses focus breathe BECAUSE you focus them, or do they focus breathe TO focus?

NOT asking about true cine lenses or floating-element ultrawides here.

(NB while this might seem like a pure optics design question not related to photography, it can become relevant when assessing how to best choose or modify lens adapters).