In this work, we present the results of first-of-their-kind nonlinear local gyrokinetic simulations of electromagnetic turbulence at mid-radius in the burning plasma phase of the conceptual high-β, reactor-scale, tight-aspect-ratio tokamak STEP (Spherical Tokamak for Energy Production). A prior linear analysis in D.Kennedy et al. submitted to Nucl. Fusion [1] reveals the presence of unstable hybrid kinetic ballooning modes and subdominant microtearing modes at binormal scales approaching the ion-Larmor radius. Local nonlinear gyrokinetic simulations, using three different codes, are in qualitative and quantitative agreement and suggest that hybrid kinetic ballooning modes drive very large turbulent transport in the absence of equilibrium flow shear. The heat flux rises to values that exceed the available heating power by orders of magnitude and the turbulent eddies are highly extended radially so that they may not be well described by the local gyrokinetic model. The saturated transport fluxes are extremely sensitive to equilibrium flow shear, and diamagnetic levels of flow shear can suppress the fluxes to more reasonable values on the chosen surface. Given this sensitivity there is a large uncertainty in the saturated fluxes. The possible transport impact of the subdominant microtearing modes is also analysed in isolation by artificially and unphysically removing compressional magnetic perturbations from nonlinear calculations, to suppress the dominant hybrid kinetic ballooning mode. The microtearing heat flux is found to saturate at negligible values, though we cannot exclude the possibility that microtearing turbulence may be more transport relevant in other regions of parameter space.