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. Phys. Rev. D 105, 123525 (2022)), 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 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 ≡M500 c/MSZ) from our measurements, finding B =1.8 ±0.1 when adopting the Planck-preferred cosmological parameters. We additionally find that our measurements are consistent with a nonzero redshift evolution of B , with the correct sign and sufficient magnitude to explain the mass bias necessary to reconcile cluster count measurements with the Planck-preferred cosmology. Our analysis introduces a model for the impact of intrinsic alignments (IAs) of galaxy shapes on the shear-tSZ correlation. We show that IA can have a significant impact on these correlations at current noise levels.