When Stars Mimic Monsters: Spectral Evidence for an $η$ Carinae-like Giant Eruption in SBS 0335$-$052 E

SBS 0335$-$052 E is an extremely low-metallicity ($Z\sim0.04\,Z_{\odot}$) blue compact dwarf galaxy. An active galactic nucleus has been proposed to explain the broad H$α$ emission and near-infrared (NIR) time variability in super star clusters 1 and 2 (SSCs 1&2). However, Peng et al. discovered broad wings in the forbidden [O III] $\lambda5007$ emission (up to $\sim5\,000\,\rm{km\,s^{-1}}$), challenging the broad-line region interpretation. We present new KCWI/KCRM integral-field spectroscopy to directly compare spectra across multiple SSCs. The nebula surrounding SSCs 1&2 shows unique features. The Ly$β$-pumped O I $\lambda8446$ emission constrains $τ_{\rm\,Lyα}\sim10^8$. Multiple ionization states of iron are detected from Fe$^{+}$ to Fe$^{+4}$. Stellar photoionization models can reproduce the [Fe III]/[Fe II] and [Fe IV]/[Fe III] line ratios at high density ($n_e\sim10^6\,\rm{cm^{-3}}$), but they fail to account for most of the [Fe V] emission. The broad H$α$ wings exhibit an exponential profile; the asymmetric wings extend from $\sim-5\,000\,\rm{km\,s^{-1}}$ to $\sim10\,000\,\rm{km\,s^{-1}}$. Thomson scattering in a radially expanding medium provides a good fit with $v_w\sim200\,\rm{km\,s^{-1}}$, optical depth $τ_e\sim10$, and an outer to inner radius of 10. Enhanced N/O and potentially depleted Fe/O ratios are consistent with CNO-cycled ejecta from massive stars and with dust formation, respectively. We propose that mass loss from a massive star interacting with its circumstellar medium drives a shock that powers the NIR variability, the luminous X-ray point source, and the [Fe V] emission. If confirmed, the proposed stellar eruption would be a distant example of an $η$ Carinae-like giant eruption, and the first in an ultra-low metallicity environment.