We explore the influence of non-axisymmetric modes on the dynamics of the collapsed core of rotating, magnetized high-mass stars in three-dimensional simulations of a rapidly rotating star with an initial mass of $M_{ZAMS}$ = 35 solar masses endowed with four different pre-collapse configurations of the magnetic field, ranging from moderate to very strong field strength and including the field predicted by the stellar evolution model. The model with the weakest magnetic field achieves shock revival due to neutrino heating in a gain layer characterized by a large-scale, hydrodynamic m = 1 spiral mode. Later on, the growing magnetic field of the proto-neutron star launches weak outflows into the early ejecta. Their orientation follows the evolution of the rotational axis of the proto-neutron star, which starts to tilt from the original orientation due to the asymmetric accretion flows impinging on its surface. The models with stronger magnetization generate mildly relativistic, magnetically driven polar outflows propagating over a distance of $10^4$ km within a few 100 ms. These jets are stabilized against disruptive non-axisymmetric instabilities by their fast propagation and by the shear of their toroidal magnetic field. Within the simulation times of around 1 s, the explosions reach moderate energies and the growth of the proto-neutron star masses ceases at values substantially below the threshold for black hole formation, which, in combination with the high rotational energies, might suggest a possible later proto-magnetar activity.
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