Extreme stripped-envelope supernovae (SESNe), including Type Ic superluminous supernovae (SLSNe-I), broad-line Type Ic SNe (SNe Ic-BL), and fast blue optical transients (FBOTs), are widely believed to harbor a newborn fast-spinning highly-magnetized neutron star (``magnetar''), which can lose its rotational energy via spin-down processes to accelerate and heat the ejecta. The progenitor(s) of these magnetar-driven SESNe, and the origin of considerable angular momentum (AM) in the cores of massive stars to finally produce such fast-spinning magnetars upon core-collapse are still under debate. Popular proposed scenarios in the literature cannot simultaneously explain their event rate density, SN and magnetar parameters, and the observed metallicity. Here, we perform a detailed binary evolution simulation that demonstrates that tidal spin-up helium stars with efficient AM transport mechanism in close binaries can form fast-spinning magnetars at the end of stars' life to naturally reproduce the universal energy-mass correlation of these magnetar-driven SESNe. Our models are consistent with the event rate densities, host environments, ejecta masses, and energetics of these different kinds of magnetar-driven SESNe, supporting that the isolated common-envelope formation channel could be a major common origin of magnetar-driven SESNe. The remnant compact binary systems of magnetar-driven SESNe are progenitors of some gravitational-wave transients and galactic systems.

Main text (20 pages, 5 Figures) and Supplementary Information (31 pages, 19 Figures, 2 tables)