  Context. Gaia DR3 has offered the scientific community a remarkable dataset
of approximately one million spectra acquired with the Radial Velocity
Spectrometer (RVS) in the Calcium II triplet region, that is well-suited to
identify very metal-poor (VMP) stars. However, over 40% of these spectra have
no released parameters by Gaia's GSP Spec pipeline in the domain of VMP stars,
whereas VMP stars are key tracers of early Galactic evolution. Aims. We aim to
provide spectroscopic metallicities for VMP stars using Gaia RVS spectra,
thereby producing a catalogue of bright VMP stars distributed over the full sky
that can serve as the basis to study early chemical evolution throughout the
Galaxy. Methods. We select VMP stars using photometric metallicities from the
literature and analyse the Gaia RVS spectra to infer spectroscopic
metallicities for these stars. Results. The inferred metallicities agree very
well with literature high-resolution metallicities with a median systematic
offset of 0.1 dex and standard deviation of $\sim$0.15 dex. The purity of this
sample in the VMP regime is $\sim$80% with outliers representing a mere
$\sim$3%. Conclusions. We make available an all-sky catalogue of $\sim$1500
stars with reliable spectroscopic metallicities down to [Fe/H]$\sim$-4.0, of
which $\sim$1000 are VMP stars. More than 75% of these stars have either no
metallicity value in the literature to date or are flagged to be unreliable in
their literature metallicity estimates. This catalogue of bright (G<13) VMP
stars is three times larger than the current sample of well-studied VMP stars
in the literature in this magnitude range, making it ideal for high-resolution
spectroscopic follow-up and to study the properties of VMP stars in different
parts of our Galaxy.
