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This manuscript presents a multilevel analysis of gamma-ray bursts (GRBs). We focus on the plateau phase, which is often observed in the light curves (LCs) of GRBs. We discuss its observational properties and then thoroughly examine possible theoretical models to explain them. Inspired by the limitations of many currently known models, we introduce a novel scenario of an LC powered by the kinetic energy of a rotating black hole (BH). We investigate observational correlations between the properties of GRBs across the gamma, X-ray, and optical bands during the prompt and plateau phases of their LCs. Our analysis includes all GRBs with known redshifts detected by the Neil Gehrels Swift Observatory (Swift) and the Fermi Gamma-ray Space Telescope (Fermi), as well as ground-based optical telescopes. We identify a tight correlation with the R^2 coefficient of ~0.89 for the three-dimensional Dainotti relation between the luminosity at the end of the plateau, its duration measured by Swift, and the peak luminosity measured by Fermi in the 10-1000 keV band. When accounting for redshift evolution, we achieve very small intrinsic scatter $\sigma_{int}=0.25\pm0.04$ (~43% reduction compared to the previous results). Additionally, we explore correlations involving the optical luminosity at the end of the plateau, yielding promising results. We investigate the clustering of different classes of GRBs in the investigated parameter space and discuss its impact on the aforementioned correlations as well as $E_{iso}$-$E^*_{peak}$ correlation. Notably, we demonstrate how to use the correlations as a powerful class discriminator. Finally, we discuss the theory supporting the evidence of the plateau emission. We present a new paradigm for the GRB plateau: energy extraction from a quickly rotating black hole (BH) via spin-down by a magnetically arrested disk (MAD). The abstract is continued in the comments.