The Gaia-Kepler-TESS-Host Stellar Properties Catalog: Uniform Physical Parameters for 7993 Host Stars and 9324 Planets

We present the first homogeneous catalog of $Kepler$, $K2$, and $TESS$ host stars and the corresponding catalog of exoplanet properties, which contain 7993 stars and 9324 planets, respectively. We used isochrone fitting and $Gaia$ DR3 photometry, parallaxes, and spectrophotometric metallicities to compute precise, homogeneous $T_{\mathrm{eff}}$, $\log g$, masses, radii, mean stellar densities, luminosities, ages, distances, and V-band extinctions for 3248, 565, and 4180 $Kepler$, $K2$, and $TESS$ stars, respectively. We compared our stellar properties to studies using fundamental and precise constraints, such as interferometry and asteroseismology, and find residual scatters of 2.8%, 5.6%, 5.0%, and 31%, with offsets of 0.2%, 1.0%, 1.2%, and 0.7% between our $T_{\mathrm{eff}}$, radii, masses, and ages and those in the literature, respectively. In addition, we compute planet radii, semimajor axes, and incident fluxes for 4281, 676, and 4367 $Kepler$, $K2$, and $TESS$ planets, respectively, and find that the exoplanet radius gap is less prominent in the $K2$, $TESS$, and combined samples than it is in the $Kepler$ sample alone. We suspect this difference is largely due to heterogeneous planet-to-star radius ratios, shorter time baselines of $K2$ and $TESS$, and smaller sample sizes. Finally, we identify a clear radius inflation trend in our large sample of hot Jupiters and find 150 hot sub-Neptunian desert planets, in addition to a population of over 400 young host stars as potential opportunities for testing theories of planet formation and evolution.