  The Transiting Exoplanet Survey Satellite (TESS) has discovered hundreds of
new worlds, with TESS planet candidates now outnumbering the total number of
confirmed planets from $\textit{Kepler}$. Owing to differences in survey
design, TESS continues to provide planets that are better suited for subsequent
follow-up studies, including mass measurement through radial velocity (RV)
observations, compared to Kepler targets. In this work, we present the
TESS-Keck Survey's (TKS) Mass Catalog: a uniform analysis of all TKS RV survey
data which has resulted in mass constraints for 126 planets and candidate
signals. This includes 58 mass measurements that have reached $\geq5\sigma$
precision. We confirm or validate 32 new planets from the TESS mission either
by significant mass measurement (15) or statistical validation (17), and we
find no evidence of likely false positives among our entire sample. This work
also serves as a data release for all previously unpublished TKS survey data,
including 9,204 RV measurements and associated activity indicators over our
three year survey. We took the opportunity to assess the performance of our
survey, and found that we achieved many of our goals including measuring the
mass of 38 small ($<4R_{\oplus}$) planets, nearly achieving the TESS mission's
basic science requirement. In addition, we evaluated the performance of the
Automated Planet Finder (APF) as survey support and observed meaningful
constraints on system parameters due to its more uniform phase coverage.
Finally, we compared our measured masses to those predicted by commonly used
mass-radius relations and investigated evidence of systematic bias.
