Understanding the distribution of cosmic baryons is crucial for advancing cosmology and galaxy formation. Localized Fast Radio Bursts (FRBs) are a promising new probe of the diffuse gas, but measurements thus far have been limited by small sample size. In this work, we measure the FRB dispersion measure (DM)-galaxy cross correlation with 130 localized FRBs, including new spectroscopic host redshifts from the DSA-110, and the DESI Legacy Survey Bright Galaxy Sample. We detect this signal at the highest significance to date ($6.5\sigma$) in both configuration and harmonic space. By comparing to simulations and a halo model, we demonstrate that this statistic can constrain the strength of baryonic feedback. Our measurements disfavor a no-feedback scenario in which gas traces the underlying dark matter at $\sim$,$9\sigma$. In addition to small scale feedback, this represents one of the first direct measurements of the clustering of electrons on scales larger than a few Mpc. We compare our measurement to recent kinematic Sunyaev-Zeldovich effect (kSZ) studies, which show good agreement despite the differences in observational methods and sample selection. Finally, we make a first attempt at breaking the kSZ optical depth degeneracy with FRBs, jointly measuring the growth rate of large-scale structure $f{\sigma }_8$. With future samples, FRB two-point statistics will provide precision constraints on the distribution of cosmic baryons and complement other probes.