  Primordial magnetic fields (PMFs) may significantly influence 21-cm physics
via two mechanisms: (i) magnetic heating of the intergalactic medium (IGM)
through ambipolar diffusion (AD) and decaying magnetohydrodynamic turbulence
(DT), (ii) impact on the star formation rate density (SFRD) through small-scale
enhancement of the matter power spectrum. In this analysis, we integrate both
of these effects within a unified analytical framework and use it to determine
upper bounds on the parameter space of a nearly scale-invariant non-helical PMF
in the light of the global 21-cm signal observed by EDGES. Our findings reveal
that the joint consideration of both effects furnishes constraints of the order
$B_0\lesssim\mathcal{O}(10^{-2})$ nG on the present-day magnetic field
strength, which are considerably tighter compared to earlier analyses. We
subsequently explore the prospects of detecting such a magnetized 21-cm power
spectrum at the upcoming SKA-Low mission. For the relevant parameters of the
PMF ($B_0$ and $n_{\!_{B}}$) and the excess radio background ($\xi$), SNR
estimation and Fisher forecast analysis indicate that it may be possible to
constrain these three parameters with relative $1\sigma$ uncertainties
$\lesssim10\%$ and an associated SNR $\gtrsim10$ at SKA-Low. This also leads to
possible correlations among these three parameters, thus revealing intriguing
trends of interplay among the various physical processes involved.
