Context. Satellite galaxies experience multiple physical processes when interacting with their host halos, often leading to the quenching of star formation. In the Local Group, satellite quenching has been shown to be highly efficient, affecting nearly all satellites except the most massive ones. While recent surveys study Milky Way-analogs to assess how representative our Local Group is, the dominant physical mechanisms behind satellite quenching in Milky Way-mass halos remain under debate. Aims. We analyze satellite quenching within the same Milky Way-mass halo simulated using various widely used astrophysical codes, each using different hydrodynamic methods and implementing different supernovae feedback recipes. The goal is to determine whether quenched fractions, quenching timescales, and the dominant quenching mechanisms are consistent across codes or if they show sensitivity to the specific hydrodynamic method and supernovae feedback physics employed. Methods. We used a subset of high-resolution cosmological zoom-in simulations of a Milky Way-mass halo from the multiple-code AGORA CosmoRun suite. Our analysis focuses on comparing satellite quenching across the different models and against observational data. We also analyzed the dominant mechanisms driving satellite quenching in each model. Results. We find that the quenched fraction is consistent with the latest SAGA Survey results within its 1σ host-to-host scatter across all the models. Regarding quenching timescales, all the models reproduce the trend observed in the ELVES survey, Local Group observations, and previous simulations: The less massive the satellite, the shorter its quenching timescale. All of our models converge on the dominant quenching mechanisms: Strangulation halts cold gas accretion in all satellites, while ram pressure stripping is the predominant mechanism for gas removal, and it is particularly effective in satellites with M∗ < 108 M . Nevertheless, the efficiency of the stripping mechanisms differs among the codes, showing a strong sensitivity to the different supernovae feedback implementations and/or hydrodynamic methods employed.