The engulfment of a neutron star (NS) by a massive companion initiates a highly dynamic common-envelope (CE) evolution phase. As the NS spirals into the dense stellar core, it is subjected to hypercritical accretion rates that threaten to rapidly collapse the NS into a black hole (BH). However, if the infalling envelope possesses sufficient angular momentum and magnetic fields, the NS might survive longer and launch feedback-driving jets. To investigate this, we perform fully coupled, axisymmetric General Relativistic Magnetohydrodynamic (GRMHD) simulations of hyperaccreting NSs, featuring energy-integrated two-moment neutrino transport and a 13-isotope nuclear reaction network. We systematically vary the envelope rotation profile and the magnetic field strength of the NS surface ($B_{\rm surf} \sim 5 \times 10^{10} - 5 \times 10^{13}$~G). In non-magnetised models, we find that envelope rotation naturally forms a centrifugal barrier and a geometrically thick accretion disk, which suppresses the mass accretion rate and lowers the neutrino luminosity; conversely, the intrinsic spin of the NS has a negligible global impact. In magnetised models, the differential rotation of the accretion flow vigorously amplifies the toroidal magnetic field via the $\Omega$-effect, driving the expansion of magnetic towers. Crucially, for strong initial surface magnetic fields ($B_{\rm surf} \gtrsim 2.3 \times 10^{13}$~G), the intense magnetic pressure could completely halt the accretion flow at the NS surface and evacuates a low-density polar funnel. We conclude that while this highly magnetised NS engine successfully delays prompt BH formation and may launche low-power precursor jets (with powers up to ${\sim} 10^{46}~{\rm erg/s}$) capable of generating observable X-ray flares, it lacks the energy budget to unbind the massive envelope, potentially setting the stage for a subsequent BH-driven explosion.