SMACS J0723.3-7327 is the first galaxy cluster lens observed by James Webb Space Telescope (JWST). Based on its early release observation data, several groups have reported the results on strong lensing analysis and mass distribution of this cluster. The new lens model dramatically improves upon previous results, thanks to JWST's unprecedented sensitivity and angular resolution. However, limited by the angular coverage of the JWST data, the strong lensing models only cover the central region. Conducting an X-ray analysis on the hot intracluster medium (ICM) is necessary to obtain a more complete constraint on the mass distribution in this very massive cluster. In this work, we perform a comprehensive X-ray analysis of SMACS J0723.3-7327 with an aim to obtain accurate ICM hydrostatic mass measurements, using the X-ray data from Spectrum Roentgen Gamma (SRG)/eROSITA and Chandra X-ray observatories. By comparing the hydrostatic mass profile with the strong lensing model, we aim to provide the most reliable constraint on the distribution of mass up to R_500_. Thanks to the eROSITA all-sky survey and Chandra, which provide high signal-to-noise ratio (S/N) and high angular resolution data, respectively, we were able to constrain the ICM gas density profile and temperature profile with good accuracy both in the core and to the outskirts. With the density and temperature profiles, we computed the hydrostatic mass profile, which was then projected along the line of sight to compare with the mass distribution obtained from the recent strong lensing analysis based on JWST data. We also deprojected the strong lensing mass distribution using the hydrostatic mass profile obtained in this work. The X-ray results obtained from eROSITA and Chandra are in very good agreement. The hydrostatic mass profiles we measured in this work, both projected and deprojected, are in good agreement with recent strong lensing results based on JWST data, at all radii. The projected hydrostatic mass within 128kpc (the estimated Einstein radius) is 8.0+/-0.7x10^13^M_{sun}_, consistent with the strong lensing mass reported in recent literature. With the hydrostatic mass profile, we measured R_2500_=0.54+/-0.04Mpc and M_2500_=(3.5+/-0.8)x10^14^M_{sun}_, while the R_500_ and M_500_ are 1.32+/-0.23Mpc and (9.8+/-5.1)x10^14^M_{sun}, with a relatively larger error bar due to the rapidly decreasing S/N in the outskirts. We also find that the radial acceleration relation in SMACS J0723.3-7327 is inconsistent with the RAR for spiral galaxies, implying that the latter is not a universal property of gravity across all mass scales.