  Omega Centauri ($\omega$ Cen) is the most massive globular cluster of the
Milky Way and has been the focus of many studies that reveal the complexity of
its stellar populations and kinematics. However, most previous studies have
used photometric and spectroscopic datasets with limited spatial or magnitude
coverage, while we aim to investigate it having full spatial coverage out to
its half-light radius and stars ranging from the main sequence to the tip of
the red giant branch. This is the first paper in a new survey of $\omega$ Cen
that combines uniform imaging and spectroscopic data out to its half-light
radius to study its stellar populations, kinematics, and formation history. In
this paper, we present an unprecedented MUSE spectroscopic dataset combining 87
new MUSE pointings with previous observations collected from guaranteed time
observations. We extract spectra of more than 300,000 stars reaching more than
two magnitudes below the main sequence turn-off. We use these spectra to derive
metallicity and line-of-sight velocity measurements and determine robust
uncertainties on these quantities using repeat measurements. Applying quality
cuts we achieve signal-to-noise ratios of 16.47/73.51 and mean metallicity
errors of 0.174/0.031 dex for the main sequence stars (18 mag $\rm <
mag_{F625W}<$22 mag) and red giant branch stars (16 mag $<\rm mag_{F625W}<$10
mag), respectively. We correct the metallicities for atomic diffusion and
identify foreground stars. This massive spectroscopic dataset will enable
future studies that will transform our understanding of $\omega$ Cen, allowing
us to investigate the stellar populations, ages, and kinematics in great
detail.
