Right, the Marked focal length only applies to infinity focus (and it is only nominal then, rounded off a bit).
If you focus closer than infinity, the lens lengthens to do that, and the focal length always changes a bit, on any lens, zoom, prime, whatever. The marked focus length number only applies to infinity focus.
This breathing effect is speaking of zooming. Focused at the same close point (where it is no longer precise anyway), zooming can change it again, a little.
Come on guys, we use DSLR, and the viewfinder shows exactly what we are getting. Adjust for that. The exact specific number is not important to us, has no real meaning to us.