  Gravitational waves (GWs) provide a new avenue to test Einstein's General
Relativity (GR) using the ongoing and upcoming GW detectors by measuring the
redshift evolution of the effective Planck mass proposed by several modified
theories of gravity. We propose a model-independent, data-driven approach to
measure any deviation from GR in the GW propagation effect by combining
multi-messenger observations of GW sources accompanied by EM counterparts,
commonly known as bright sirens (Binary Neutron Star (BNS) and Neutron Star
Black Hole systems (NSBH)). We show that by combining the GW luminosity
distance measurements from bright sirens with the Baryon Acoustic Oscillation
(BAO) measurements derived from galaxy clustering, and the sound horizon
measurements from the Cosmic Microwave Background (CMB), we can make a
data-driven reconstruction of deviation of the variation of the effective
Planck mass (jointly with the Hubble constant) as a function of cosmic
redshift. Using this technique, we achieve a precise measurement of GR with
redshift (z) with a precision of approximately $7.9\%$ for BNSs at redshift
z=0.075 and $10\%$ for NSBHs at redshift z=0.225 with 5 years of observation
from LIGO-Virgo-KAGRA network of detectors. Employing Cosmic Explorer and
Einstein Telescope for just 1 year yields the best precision of about $1.62\%$
for BNSs and $2\%$ for NSBHs at redshift z=0.5 on the evolution of the
frictional term, and a similar precision up to z=1. This measurement can
discover potential deviation from any kind of model that impacts GW propagation
with ongoing and upcoming observations.
