The tip of the red giant branch (TRGB) is a standard candle that can be used to help refine the determination of the Hubble constant. Gaia Data Release 3 (DR3) provides synthetic photometry constructed from low-resolution BP/RP spectra for Milky Way field stars that can be used to directly calibrate the luminosity of the TRGB in the Johnson-Cousins I band, where the TRGB is least sensitive to metallicity. We calibrate the TRGB luminosity using a two-dimensional maximum likelihood algorithm with field stars and Gaia synthetic photometry and parallaxes. For a high-contrast and low-contrast break (characterized by the values of the contrast parameter R or the magnitude of the break {beta}), we find M^TRGB^_I_=-4.02 and -3.92mag respectively, or a midpoint of -3.970_-0.024_^+0.042^(sys)+/-0.062(stat)mag. This measurement improves upon the TRGB measurement from Li+ (2022, J/ApJ/939/96), as the higher precision photometry based on Gaia DR3 allows us to constrain two additional free parameters of the luminosity function. We also investigate the possibility of using Gaia DR3 synthetic photometry to calibrate the TRGB luminosity with {omega} Centauri, but find evidence of blending within the inner region for cluster member photometry that precludes accurate calibration with Gaia DR3 photometry. We instead provide an updated TRGB measurement of m^TRGB^_I_=9.82+/-0.04mag in {omega} Centauri using ground-based photometry from the most recent version of the database described in Stetson+ (2019, J/MNRAS/485/3042), which gives M^TRGB^_I_=-3.97+/-0.04(stat)+/-0.10(sys)mag when tied to the Gaia EDR3 parallax distance from the consensus of Vasiliev & Baumgardt (2021, J/MNRAS/505/5978), Soltis+ (2021, J/ApJ/908/L5), and Maiz Apellaniz J. (2022A&A...657A.130M).