Massive galaxies are expected to host extended halos of hot gas that contain a substantial fraction of their baryons and feedback energy. X-ray observations probe the dense, X-ray-bright component of this circumgalactic medium (CGM), while the thermal Sunyaev-Zel'dovich (SZ) effect is also sensitive to lower-density gas through its integrated thermal pressure. We present the first spatially resolved joint X-ray and SZ analysis of a massive isolated disk galaxy, using deep XMM-Newton observations of NGC 4594 from the X-raying the Accretion Reservoir Transferred to the ATmosphere Orbiting a Massive Spiral (XART-ATOMS) program, together with multiple independent Planck-based SZ reconstructions. The measured SZ signal in the inner halo appears to exceed the value predicted from the X-ray-derived gas properties, even after accounting for major systematic uncertainties. Our preferred interpretation is that an additional lower-density CGM component contributes little to the observed soft X-ray emission but carries substantial thermal pressure. Under a simple two-phase model in approximate pressure equilibrium, the most probable X-ray-to-SZ ratio implies that the detected X-ray-emitting gas occupies only a small fraction of the halo volume, with a characteristic filling factor of f_X ~ (4-6)x10^-3 near r 50 kpc. Such a small filling factor implies that single-phase X-ray analyses can underestimate the baryon mass contained in the hot CGM by a factor of ~2.5, while the thermal energy content of the CGM is underestimated by about one order of magnitude. The non-detection of the additional component in the X-ray spectra requires it to be very hot and/or spatially extended, so weak in the soft X-ray emissions. These results favor the presence of a "hidden" X-ray-faint hotter halo component, while alternative interpretations, including a nonthermal contribution, are not excluded.