Sr2IrO4 has often been described via a simple, one-band pseudospin-12 model subject to electron-electron interactions on a square lattice, fostering analogies with cuprate superconductors believed to be well described by a similar model. In this work we argue - based on a detailed study of the low-energy electronic structure by circularly polarized spin and angle-resolved photoemission spectroscopy combined with dynamical mean-field theory calculations - that a pseudospin-12 model fails to capture the full complexity of the system. We show instead that a realistic multiband Hubbard Hamiltonian, accounting for the full correlated t2g manifold, provides a detailed description of the interplay between spin-orbital entanglement and electron-electron interactions and yields quantitative agreement with experiments. Our analysis establishes that the j3/2 states make up a substantial percentage of the low-energy spectral weight, i.e., approximately 74% as determined from the integration of the j-resolved spectral function in the 0 to -1.64eV energy range. The results in our work are of relevance not only to Ir-based materials but also more generally to multiorbital materials with closely spaced energy scales.