  We present a new set of period-absolute magnitude-metallicity (PMZ) relations
for 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. We
compiled a large dataset (over $100$ objects) of fundamental and first-overtone
RR~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 newly
calibrated PMZ relations encapsulate the most up-to-date ingredients in terms
of both data and methodology. They are aimed to be used in conjunction with
large photometric surveys targeting the Galactic bulge, including the Optical
Gravitational Lensing Experiment (OGLE), the Vista Variables in the V\'ia
L\'actea Survey (VVV), and the \textit{Gaia} catalog. In addition, our Bayesian
probabilistic approach provides accurate uncertainty estimates of the predicted
absolute magnitudes of individual RR Lyrae stars. Our derived PMZ relations
provide consistent results when compared to benchmark distances to Globular
clusters NGC\,6121 (also known as M4), NGC\,5139 (also known as omega Cen), and
Large and Small Magellanic Clouds, which are stellar systems rich in RR~Lyrae
stars. Lastly, our $K_{\rm s}$-band PMZ relations match well with the
previously published PMZ relations based on Gaia data and accurately predict
the distance toward the prototype of this class of variables, the eponymic
RR~Lyr itself.
