  We present a low-frequency (170\textendash200\,MHz) search for prompt radio
emission associated with the long GRB 210419A using the rapid-response mode of
the Murchison Widefield Array (MWA), triggering observations with the Voltage
Capture System (VCS) for the first time. The MWA began observing GRB 210419A
within 89\,s of its detection by \textit{Swift}, enabling us to capture any
dispersion delayed signal emitted by this GRB for a typical range of redshifts.
We conducted a standard single pulse search with a temporal and spectral
resolution of $100\,\upmu$s and 10\,kHz over a broad range of dispersion
measures from 1 to $5000\,\text{pc}\,\text{cm}^{-3}$, but none were detected.
However, fluence upper limits of $77\text{--}224$\,Jy\,ms derived over a pulse
width of $0.5\text{--}10$\,ms and a redshift of $0.6<z<4$ are some of the most
stringent at low radio frequencies. We compared these fluence limits to the GRB
jet-interstellar medium (ISM) interaction model, placing constraints on the
fraction of magnetic energy ($\epsilon_{\text{B}}\lesssim[0.05 \text{--}
0.1]$). We also searched for signals during the X-ray flaring activity of GRB
210419A on minute timescales in the image domain and found no emission,
resulting in an intensity upper limit of $0.57\,\text{Jy}\,\text{beam}^{-1}$,
corresponding to a constraint of $\epsilon_{\text{B}}\lesssim10^{-3}$. Our
non-detection could imply that GRB 210419A was at a high redshift, there was
not enough magnetic energy for low-frequency emission, or that the radio waves
did not escape from the GRB environment.
