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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 $ω$ Centauri ($ω$Cen). Under the assumption that $ω$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 $ω$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.