The Sunburst Arc with JWST: II. Observations of an Eta Carinae Analog at z=2.37

"Godzilla" is a peculiar object within the gravitationally lensed Sunburst Arc at $z=2.37$. Despite being very bright, it appears in only one of the twelve lensed images of the source galaxy, and shows exotic spectroscopic properties not found in any other clumps. We use JWST's unique combination of spatial resolution and spectroscopic sensitivity to provide a unified, coherent explanation of the physical nature of Godzilla. We measure fluxes and kinematic properties of rest-optical emission lines in Godzilla and surrounding regions. Using standard line ratio-based diagnostic methods in combination with NIRCam imaging and ground based rest-UV spectra, we characterize Godzilla and its surroundings. Among around 60 detected lines, we find a cascade of strong O I lines pumped by intense Ly$\beta$ emission, as well as Ly$\alpha$-pumped rest-optical Fe II lines, reminiscent of the Weigelt blobs in the local LBV star Eta Carinae. Spectra and images of Godzilla and two faint adjacent images, and the detection of a low-surface brightness foreground galaxy in the NIRCam data, support the interpretation that Godzilla is an extremely magnified object due to the alignment with lensing caustics. We find that Godzilla is part of a previously identified clump, comprising $\sim10 - 25$ % of it, with magnifications in the range of $\approx600-25,000$ depending on the models and images in comparison. The unique O I source in Godzilla is well explained by a non-erupting LBV accompanied by a hotter companion and/or gas condensations exposed to more intense radiation compared to the Weigelt blobs. If Godzilla is confirmed to contain an LBV star, it expands the distance to the furthest known LBV from a dozen Mpc to several Gpc.