  Star formation rates (SFRs), gas-phase metallicities, and stellar masses are
crucial for studying galaxy evolution. The different relations resulting from
these properties give insights into the complex interplay of gas inside
galaxies and their evolutionary trajectory and current characteristics. We aim
to characterize these relations at $z\sim 0.3$, corresponding to a 3-4 Gyr
lookback time. We utilized optical integral field spectroscopy of 65
emission-line galaxies from the MAGPI survey at a redshift of $0.28<z<0.35$ and
spanning a total stellar mass range of $8.2<\log(M_{*}/M_{\odot}) < 11.4$. We
derived the resolved star formation main sequence (rSFMS), resolved mass
metallicity relation (rMZR), and resolved fundamental metallicity relation
(rFMR) at $z\sim 0.3$. We find a relatively shallow rSFMS slope of $\sim 0.425
\pm 0.014$ compared to the expected slope at this redshift for an ordinary
least square (OLS) fitting routine. For an orthogonal distance regression (ODR)
routine, a much steeper slope of $\sim 1.162 \pm 0.022$ is measured. We confirm
the existence of an rMZR at $z\sim 0.3$ with an average metallicity located
$\sim 0.03$ dex above the local Universe's metallicity. Via partial correlation
coefficients, evidence is found that the local metallicity is predominantly
determined by the stellar mass surface density and has a weak secondary
(inverse) dependence on the SFR surface density $\Sigma_{SFR}$. Additionally, a
significant dependence of the local metallicity on the total stellar mass
$M_{*}$ is found. Furthermore, we find that the stellar mass surface density
$\Sigma_{*}$ and $M_{*}$ have a significant influence in determining the
strength with which $\Sigma_{SFR}$ correlates with the local metallicity. We
observe that at lower stellar masses, there is a tighter correlation between
$\Sigma_{SFR}$ and the gas-phase metallicity, resulting in a more pronounced
rFMR.
