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We present a new set of period-absolute magnitude-metallicity (PMZ) relationsfor single-mode RR Lyrae stars calibrated for the optical $G_{\rm BP}$, $V$,$G$, $G_{\rm RP}$, near-infrared $I$, $J$, $H$, and $K_{\rm s}$ passbands. Wecompiled a large dataset (over $100$ objects) of fundamental and first-overtoneRR~Lyrae pulsators consisting of mean intensity magnitudes, reddenings,pulsations properties, iron abundances, and parallaxes measured by the\textit{Gaia} astrometric satellite in its third data release. Our newlycalibrated PMZ relations encapsulate the most up-to-date ingredients in termsof both data and methodology. They are aimed to be used in conjunction withlarge photometric surveys targeting the Galactic bulge, including the OpticalGravitational Lensing Experiment (OGLE), the Vista Variables in the V\'iaL\'actea Survey (VVV), and the \textit{Gaia} catalog. In addition, our Bayesianprobabilistic approach provides accurate uncertainty estimates of the predictedabsolute magnitudes of individual RR Lyrae stars. Our derived PMZ relationsprovide consistent results when compared to benchmark distances to Globularclusters NGC\,6121 (also known as M4), NGC\,5139 (also known as omega Cen), andLarge and Small Magellanic Clouds, which are stellar systems rich in RR~Lyraestars. Lastly, our $K_{\rm s}$-band PMZ relations match well with thepreviously published PMZ relations based on Gaia data and accurately predictthe distance toward the prototype of this class of variables, the eponymicRR~Lyr itself.

The Galactic Bulge exploration I.: The  period-absolute\,magnitude-metallicity relations for RR~Lyrae stars for  $G_{\rm BP}$, $V$, $G$, $G_{\rm RP}$, $I$, $J$, $H$, and $K_{\rm s}$  passbands using $Gaia$ DR3 parallaxes