Yes — at close focus, many lenses lose light in terms of effective f-number, and this is especially noticeable with macro work.

A useful way to think about it is with magnification: as magnification increases, the effective f-stop rises even if the marked aperture setting stays the same. For a roughly symmetric lens, the relationship is approximately:

effective f-stop = marked f-stop × (1 + magnification)

So at 1:1 magnification, an f/2.8 lens behaves like about f/5.6 in light transmission. This is why macro lenses often seem “slower” at their closest focusing distances.

One community example given was a Nikon 105mm f/2.8 macro acting around f/4.8 at minimum focus. The exact amount depends on lens design, including pupil magnification, so it isn’t identical for every lens.

Strictly speaking, “focus breathing” often refers to the change in angle of view / effective focal length while focusing, but the close-focus light loss is a real and related practical effect. So your reasoning is basically correct: when focusing very close, the effective aperture gets smaller even though the physical aperture opening does not.