  Collapsing supermassive stars (SMSs) with masses $M \gtrsim 10^{4-6}M_\odot$
have long been speculated to be the seeds that can grow and become supermassive
black holes (SMBHs). We previously performed GRMHD simulations of marginally
stable magnetized $\Gamma = 4/3$ polytropes uniformly rotating at the
mass-shedding limit to model the direct collapse of SMSs. These configurations
are supported entirely by thermal radiation pressure and model SMSs with $M
\gtrsim 10^{6}M_\odot$. We found that around $90\%$ of the initial stellar mass
forms a spinning black hole (BH) surrounded by a massive, hot, magnetized
torus, which eventually launches an incipient jet. Here we perform GRMHD
simulations of $\Gamma \gtrsim 4/3$, polytropes to account for the perturbative
role of gas pressure in SMSs with $M \lesssim 10^{6}M_\odot$. We also consider
different initial stellar rotation profiles. The stars are initially seeded
with a dynamically weak dipole magnetic field that is either confined to the
stellar interior or extended from its interior into the stellar exterior. We
find that the mass of the BH remnant is $90\%-99\%$ of the initial stellar
mass, depending sharply on $\Gamma -4/3$ as well as on the initial stellar
rotation profile. After $t\sim 250-550M\approx 1-2\times 10^3(M/10^6M_\odot)$s
following the BH formation, a jet is launched and it lasts for $\sim
10^4-10^5(M/10^6M_\odot)$s, consistent with the duration of long gamma-ray
bursts. Our results suggest that the Blandford-Znajek mechanism powers the jet.
They are also in agreement with our proposed universal model that estimates
accretion rates and luminosities that characterize magnetized BH-disk remnant
systems that launch a jet. This model helps explain why the outgoing
luminosities for vastly different BH-disk formation scenarios all reside within
a narrow range ($\sim 10^{52 \pm 1} \rm erg/s$), roughly independent of $M$.
