  Recent compilations of NIRSpec emission line galaxies have shown a mild
redshift evolution of the FMR at $z > 4$, indicating that the FMR alone is not
fully capable of capturing the redshift evolution of the mass-metallicity
relation: $z > 4$ galaxies appear more metal-poor than the FMR predictions.
There is evidence that the most metal-deficient high-redshift galaxies are also
the most compact. In this work, we further investigate this anti-correlation by
leveraging the wealth of data gathered through the first cycle of JWST. We
compile a sample of 427 $z > 3$ galaxies covered by both the NIRSpec prism and
NIRCam short-wavelength photometry, consisting of 334 galaxies from the
publicly available programs and 93 galaxies from the first data release of the
JADES program. We use this sample to infer the redshift evolution of the FMR
from $z = 3$ to $z \sim 10$, further confirming the previously reported mild
redshift evolution. We measure the rest-ultraviolet (UV) sizes of $z > 4$
galaxies, inferring the mass-size relation at $z = 4-10$ with a power-law slope
of $0.21 \pm 0.04$. We investigate the redshift evolution of the mass-size
relation, finding that at a fixed stellar mass, higher redshift galaxies appear
more compact. The degree of this redshift evolution depends on the stellar
mass, with the lowest mass galaxies showing the strongest redshift evolution
and the most massive galaxies ($\log(M_{\star}/M_{\odot}) > 9$) showing no
redshift evolution. We investigate the anti-correlation between the compactness
of galaxies and their gas-phase metallicities, finding that the more compact
galaxies appear more metal-deficient and therefore more offset from the local
calibration of the FMR. (abridged)
