The Kondo effect emerges when a localized spin is screened by conduction electrons, giving rise to a strongly-correlated many-body ground state. In this work, we investigate this phenomenon in a GaAs/AlGaAs quantum dot, focusing on the spatial extension of the Kondo screening cloud in the electron reservoirs. To probe its properties, the dot is coupled to an electronic Fabry-Pérot interferometer, enabling controlled modulation of the density of states at the Fermi level. The observation of Kondo temperature oscillations indicates a Kondo screening length comparable to the cavity size. Furthermore, we explore how the coupling asymmetry with the two reservoirs affects both the amplitude and the phase of the conductance oscillations, revealing a subtle interplay between coherent transport and Kondo effect.