  Abridged. Methods. We made use of the Karl G. Jansky Very Large Array (VLA)
in the B configuration at K band, and in the A configuration at both Ku and C
bands, in order to image the radio continuum emission towards 25 H$_2$O maser
sites with an angular resolution and thermal rms of the order of $0.1''$ and 10
$\mu$Jy beam$^{-1}$, respectively. These targets add to our pilot study of 11
maser sites presented in Moscadelli et al. (2016). The sample of H$_2$O maser
sites was selected among those regions having an accurate distance measurement,
obtained through maser trigonometric parallaxes, and H$_2$O maser luminosities
in excess of 10$^{-6}$ L$_{\odot}$. Results. We present high-resolution radio
continuum images of 33 sources belonging to 25 star-forming regions. In each
region, we detect radio continuum emission within a few 1000 au of the H$_2$O
masers' position; 50% of the radio continuum sources are associated with
bolometric luminosities exceeding 5 $\times$ 10$^{3}$ L$_{\odot}$, including
W33A and G240.32$+$0.07. We provide a detailed spectral index analysis for each
radio continuum source, based on the integrated fluxes at each frequency, and
produce spectral index maps with the multi-frequency-synthesis deconvolution
algorithm of CASA. The radio continuum emission traces thermal bremsstrahlung
in (proto)stellar winds and jets, with flux densities at 22 GHz below 3 mJy,
and spectral index values between $-0.1$ and 1.3. We prove a strong correlation
($r>$0.8) between the radio continuum luminosity (L$_{\rm rad}$) and the H$_2$O
maser luminosity (L$_{\rm H_2O}$) of ($\rm L_{8GHz}/mJy\times
kpc^2)=10^{3.8}\times(L_{H_2O}/L_{\odot})^{0.74}$. Since H$_2$O masers are
excited through shocks driven by (proto)stellar winds and jets, these results
provide support to the idea that the radio continuum emission around young
stars is dominated by shock-ionization.
