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The circumgalactic medium (CGM) around massive galaxies plays a crucial role in regulating star formation and feedback. Using the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) suite, we develop emulators for the X-ray surface brightness profile and the X-ray luminosity–stellar mass scaling relation, to investigate how stellar and active galactic nucleus (AGN) feedback shape the X-ray properties of the hot CGM. Our analysis shows that at CGM scales (1012 Mhalo/Me  1013, 10 r kpc−1  400), stellar feedback more significantly impacts the X-ray properties than AGN feedback within the parameters studied. Comparing the emulators to recent eROSITA All Sky Survey (eRASS) observations, it is found that stronger feedback than is currently implemented in the IllustrisTNG, SIMBA, and Astrid simulations is required to match the observed CGM properties. However, adopting these enhanced feedback parameters causes deviations in the stellar mass–halo mass relations from observational constraints below the group-mass scale. This tension suggests possible unaccounted for systematics in X-ray CGM observations or inadequacies in the feedback models of cosmological simulations.