We present the evolution of the mass-metallicity (MZ) relation at z=4-10 derived with 135 galaxies identified in JWST/NIRSpec data taken from the three major public spectroscopy programs of ERO, GLASS, and CEERS. Because there are many discrepancies between the flux measurements reported by the early ERO studies, we first establish our NIRSpec data reduction procedure for reliable emission-line flux measurements and errors, successfully explaining Balmer decrements with no statistical tensions thorough comparisons with the early ERO studies. Applying the reduction procedure to the 135 galaxies, we obtain emission-line fluxes for physical property measurements. We confirm that 10 out of the 135 galaxies with [OIII]{lambda}4363 lines have electron temperatures of ~(1.1-2.3)x10^4^K, similar to lower-z star-forming galaxies, which can be explained by heating by young massive stars. We derive the metallicities of the 10 galaxies by a direct method and the rest of the galaxies with strong lines using the metallicity calibrations of Nakajima et al. applicable for these low-mass metal-poor galaxies, anchoring the metallicities with the direct-method measurements. We thus obtain the MZ relation and star formation rate (SFR)-MZ relation over z=4-10. We find that there is a small evolution of the MZ relation from z~2-3 to z=4-10, while interestingly the SFR-MZ relation shows no evolution up to z~8 but a significant decrease at z>8 beyond the errors This SFR-MZ relation decrease at z>8 may suggest a break of the metallicity equilibrium state via star formation, inflow, and outflow, while further statistical and local-baseline studies are needed for a conclusion.