We introduce genesis-metallicity, a gas-phase metallicity measurement python software employing the direct and strong-line methods depending on the available oxygen lines. The non-parametric strong-line estimator is calibrated based on a kernel density estimate in the 4-dimensional space of O2 = [O II]λλ3727,29/Hβ; O3 = [O III]λ5007/Hβ; Hβ equivalent width EW(Hβ); and gas-phase metallicity 12+log(O/H). We use a calibration sample of 1510 galaxies at 0<z<10 with direct-method metallicity measurements, compiled from the JWST/NIRSpec and ground-based observations. In particular, we report 122 new NIRSpec direct-method metallicity measurements at z>1. We show that the O2, O3, and EW(Hβ) measurements are sufficient for a gas-phase metallicity estimate that is more accurate than 0.09 dex. Our calibration is universal, meaning that its accuracy does not depend on the target redshift. Furthermore, the direct-method module employs a non-parametric Te(O II) electron temperature estimator based on a kernel density estimate in the 5-dimensional space of O2, O3, EW(Hβ), Te(O III), and Te(O II). This Te(O II) estimator is calibrated based on 1004 spectra with detections of both [O III]λ4363 and [O II]λλ7320,30, notably reporting 20 new NIRSpec detections of the [O II]λλ7320,30 doublet. We make genesis-metallicity and its calibration data publicly available and commit to keeping both up-to-date in light of the incoming data.