Predicting the X-ray signatures of the imminent T Coronae Borealis outburst through 3D hydrodynamic modeling

T Coronae Borealis (T CrB) is a symbiotic recurrent nova with eruptions in 1866 and 1946. Mounting evidence suggests an imminent outburst, offering a rare opportunity to observe a nearby nova in detail. We constrain the circumbinary medium (CBM) by modeling inter-eruption radio observations and simulate the hydrodynamic evolution of the upcoming outburst to predict its X-ray signatures, focusing on the roles of the red giant companion, accretion disk, and equatorial density enhancement (EDE). We model thermal radio emission from a CBM composed of a spherical wind and a torus-like EDE to estimate its density. We then perform 3D hydrodynamic simulations of the nova outburst, varying explosion energy, ejecta mass, and CBM configuration. From these, we synthesize X-ray light curves and spectra as they would appear to XMM-Newton and XRISM. The CBM in T CrB is significantly less dense than in other symbiotic novae, with a mass-loss rate of $\dot{M} \approx 4 \times 10^{-9}$ M$_{\odot}$ yr$^{-1}$ for a 10 km s$^{-1}$ wind. Despite the low-density EDE, the blast is collimated along the poles by the accretion disk and EDE, producing a bipolar shock. The red giant partially shields the ejecta, forming a bow shock and hot wake. X-ray evolution proceeds through three phases: an early phase (first few hours) dominated by shocked disk material; an intermediate phase ($\sim 1$ week-1 month) driven by reverse-shocked ejecta; and a late phase dominated by shocked EDE. Soft X-rays trace shocked ejecta, hard X-rays arise from shocked ambient gas, and synthetic spectra show asymmetric, blueshifted lines due to absorption by expanding ejecta. The X-ray evolution resembles that of RS Oph and V745 Sco, with a peak luminosity of $L_\mathrm{X} \approx 10^{36}$ erg s$^{-1}$, but features a more prolonged soft X-ray phase, reflecting the lower CBM density and distinct ejecta-environment interaction.