A 0.3\% calibration of the W UMa-type contact binary luminosity based on Gaia DR3

W Ursa Majoris (W UMa)-type contact binary systems (CBs) with period--luminosity (PL) relations are valuable distance indicators. The PL relations of CBs are affected by metallicity. Here, we establish PL relations and period--luminosity--metallicity (PLZ) relations in nine bands from optical to mid-infrared ($BP$, $G$, $RP$, $J$, $H$, $K_S$, $W1$, $W2$, $W3$) and in five Wesenheit bands based on Gaia DR3 parallaxes. The dispersion of PLZ relations gradually decreases from the optical to mid-infrared bands, with the minimum dispersion of 0.138 mag. We fit the best PL relations for three bands ($W1$, $W_{G,BP,RP}$, $W_{W1,BP,RP}$) under different parallax uncertainty criteria and determine a parallax (after correction) zero point of $zp_\varpi=24\pm4$ $μ$as. After fixing the parallax zero point, we find that the total zero errors of the PL and PLZ relation are smallest when the parallax uncertainty is less than 2\%, resulting in a calibrated CB luminosity with an accuracy of 0.33\%, which is more accurate than the classical Cepheids. Furthermore, by examining the absolute magnitude residuals in different metallicity intervals, we find that the use of a linear metallicity effect is appropriate for CBs with different metallicities. These results indicate that CBs are excellent standard candles.