  We present uniformly measured stellar metallicities for 463 stars in 13 Milky
Way (MW) ultra-faint dwarf galaxies (UFDs; $M_V = -7.1$ to $-0.8$) using
narrowband CaHK (F395N) imaging taken with the Hubble Space Telescope (HST).
This represents the largest homogeneous set of stellar metallicities in UFDs,
increasing the number of metallicities in these 13 galaxies by a factor of 5
and doubling the number of metallicities in all known MW UFDs. We provide the
first well-populated MDFs for all galaxies in this sample, with [Fe/H] ranging
from -3.0 dex to -2.0 dex, and $\sigma_{\mbox{[Fe/H]}}$ ranging from 0.3 dex to
0.7 dex. We find a nearly constant [Fe/H] ~ -2.6 over 3 decades in luminosity
(~$10^2 - 10^5 L_{\odot}$), suggesting that the mass-metallicity relationship
does not hold for such faint systems. We find a larger fraction (24%) of EMP
([Fe/H]<-3.0) stars across our sample compared to the literature (14%), but
note that uncertainties in our most metal-poor measurements make this an upper
limit. We find 19% of stars in our UFD sample to be metal-rich ([Fe/H]>-2.0),
consistent with the sum of literature spectroscopic studies. MW UFDs are known
to be predominantly >13 Gyr old, meaning that all stars in our sample are truly
ancient, unlike metal-poor stars in the MW, which have a range of possible
ages. Our UFD metallicities are not well-matched to known streams in the MW,
providing further evidence that known MW substructures are not related to UFDs.
We include a catalog of our stars to encourage community follow-up studies,
including priority targets for ELT-era observations.
