2022ApJS..262....3N

We present optical-line gas metallicity diagnostics established by the combination of local SDSS galaxies and the largest compilation of extremely metal-poor galaxies (EMPGs) including new EMPGs identified by the Subaru EMPRESS survey. A total of 103 EMPGs are included, covering a large parameter space of magnitude (M_i = -19 to -7) and Hβ equivalent width (10-600 Å), i.e., wide ranges of stellar mass and star formation rate. Using reliable metallicity measurements from the direct method for these galaxies, we derive the relationships between strong optical-line ratios and gas-phase metallicity over the range of $12+\mathrm{log}({\rm{O}}/{\rm{H}})$ ≃ 6.9-8.9, corresponding to 0.02-2 solar metallicity Z_⊙. We confirm that the R23 index, ([O III]+[O II])/Hβ, is the most accurate metallicity indicator with a metallicity uncertainty of 0.14 dex over the range among various popular metallicity indicators. The other metallicity indicators show large scatters in the metal-poor range (≲0.1 Z_⊙). It is explained by our CLOUDY photoionization modeling that, unlike the R23 index, the other metallicity indicators do not use a sum of singly and doubly ionized lines and cannot trace both low- and high-ionization gas. We find that the accuracy of the metallicity indicators is significantly improved if one uses Hβ equivalent width measurements that tightly correlate with ionization states. In this work, we also present the relation of physical properties with the UV-continuum slope β and ionization production rate ξ_ion derived with GALEX data for the EMPGs and provide local anchors of galaxy properties together with the optical-line metallicity indicators that are available in the form of a machine-readable table and useful for forthcoming JWST spectroscopic studies.