  We combine spectroscopic, photometric, and astrometric information from
APOGEE data release 17 and $Gaia$ early data release 3 to perform a
self-consistent characterization of $Gaia$-Sausage/Enceladus (GSE), the remnant
of the last major merger experienced by the Milky Way, considering stars and
globular clusters (GCs) altogether. Our novel set of chemodynamical criteria to
select genuine stars of GSE yields a metallicity distribution function with a
median [Fe/H] of $-1.22$ dex and $0.23$ dex dispersion. Stars from GSE present
an excess of [Al/Fe] and [Mg/Mn] (also [Mg/Fe]) in comparison to surviving
Milky Way dwarf satellites, which can be explained by differences in
star-formation efficiencies and timescales between these systems. However,
stars from Sequoia, another proposed accreted halo substructure, essentially
overlap the GSE footprint in all analyzed chemical-abundance spaces, but
present lower metallicities. Among probable GCs of GSE with APOGEE observations
available, we find no evidence for atypical [Fe/H] spreads with the exception
of $\omega$ Centauri ($\omega$Cen). Under the assumption that $\omega$Cen is a
stripped nuclear star cluster, we estimate the stellar mass of its progenitor
to be $M_\star \approx 1.3 \times 10^9 M_\odot$, well-within literature
expectations for GSE. This leads us to envision GSE as the best available
candidate for the original host galaxy of $\omega$Cen. We also take advantage
of $Gaia$'s photometry and APOGEE metallicities as priors to determine
fundamental parameters for eight high-probability ($>$70%) GC members of GSE
via statistical isochrone fitting. Finally, the newly determined ages and
APOGEE [Fe/H] values are utilized to model the age-metallicity relation of GSE.
