Cross-correlation of DES Y3 lensing and ACT/${\it Planck}$ thermal
  Sunyaev Zel'dovich Effect II: Modeling and constraints on halo pressure
  profiles
  Hot, ionized gas leaves an imprint on the cosmic microwave background via the
thermal Sunyaev Zel'dovich (tSZ) effect. The cross-correlation of gravitational
lensing (which traces the projected mass) with the tSZ effect (which traces the
projected gas pressure) is a powerful probe of the thermal state of ionized
baryons throughout the Universe, and is sensitive to effects such as baryonic
feedback. In a companion paper (Gatti et al. 2021), we present tomographic
measurements and validation tests of the cross-correlation between galaxy shear
measurements from the first three years of observations of the Dark Energy
Survey, and tSZ measurements from a combination of Atacama Cosmology Telescope
and ${\it Planck}$ observations. In this work, we use the same measurements to
constrain models for the pressure profiles of halos across a wide range of halo
mass and redshift. We find evidence for reduced pressure in low mass halos,
consistent with predictions for the effects of feedback from active galactic
nuclei. We infer the hydrostatic mass bias ($B \equiv M_{500c}/M_{\rm SZ}$)
from our measurements, finding $B = 1.8\pm0.1$ when adopting the ${\it
Planck}$-preferred cosmological parameters. We additionally find that our
measurements are consistent with a non-zero redshift evolution of $B$, with the
correct sign and sufficient magnitude to explain the mass bias necessary to
reconcile cluster count measurements with the ${\it Planck}$-preferred
cosmology. Our analysis introduces a model for the impact of intrinsic
alignments (IA) of galaxy shapes on the shear-tSZ correlation. We show that IA
can have a significant impact on these correlations at current noise levels.
