  The CHIME/FRB project has detected hundreds of fast radio bursts (FRBs),
providing an unparalleled population to probe statistically the foreground
media that they illuminate. One such foreground medium is the ionized halo of
the Milky Way (MW). We estimate the total Galactic electron column density from
FRB dispersion measures (DMs) as a function of Galactic latitude using four
different estimators, including ones that assume spherical symmetry of the
ionized MW halo and ones that imply more latitudinal-variation in density. Our
observation-based constraints of the total Galactic DM contribution for
$|b|\geq 30^\circ$, depending on the Galactic latitude and selected model, span
87.8 - 141 pc cm^-3. This constraint implies upper limits on the MW halo DM
contribution that range over 52-111 pc cm^-3. We discuss the viability of
various gas density profiles for the MW halo that have been used to estimate
the halo's contribution to DMs of extragalactic sources. Several models
overestimate the DM contribution, especially when assuming higher halo gas
masses (~ 3.5 x 10^12 solar masses). Some halo models predict a higher MW halo
DM contribution than can be supported by our observations unless the effect of
feedback is increased within them, highlighting the impact of feedback
processes in galaxy formation.
