  We analyze the observed spatial, chemical, and dynamical distributions of
local metal-poor stars, based on photometrically derived metallicity and
distance estimates along with proper motions from the Gaia mission. Throughout
the sample volume ($|Z| \leq 6$ kpc) along the Galactic prime meridian, we
identify stellar populations with distinct properties in the metallicity versus
rotational velocity space, and model their phase-space distributions. Our
decomposition provides refined positions of individual populations in this
phase space identified in the previous papers of this series. Stars associated
with Gaia Sausage/Enceladus (GSE) exhibit a larger proportion of metal-poor
stars at greater distances from the Galactic center ($R_{\rm GC}$), with a
slope of $\Delta \langle {\rm [Fe/H]} \rangle/\Delta R_{\rm GC} = -0.05\pm0.02$
dex kpc$^{-1}$. This observed trend, along with a mild anti-correlation of a
mean rotational velocity with metallicity ($\Delta \langle v_\phi \rangle /
\Delta \langle {\rm [Fe/H]} \rangle \sim -10$ km s$^{-1}$ dex$^{-1}$), implies
that more metal-rich stars in the inner region of the GSE progenitor were
gradually stripped away, while the prograde orbit of the merger at infall
became radialized by dynamical friction. The metal-rich GSE stars are causally
disconnected in our decomposition from the Splash structure, whose stars are
mostly found in prograde orbits and exhibit a more centrally concentrated
distribution than GSE. The metal-weak thick disk shows a similar spatial
distribution as the Splash, suggesting earlier dynamical heating of stars in
the primordial disk of the Milky Way.
