Emergent superconductivity at the LaAlO₃/KTaO₃ interfaces exhibits a mysterious dependence on the KTaO₃ crystallographic orientations. Here by soft X-ray angle-resolved photoemission spectroscopy, we directly resolve the electronic structure of the LaAlO₃/KTaO₃ interfacial superconductors and the non-superconducting counterpart. We find that the mobile electrons that contribute to the interfacial superconductivity show strong k_⊥ dispersion. Comparing the superconducting and non-superconducting interfaces, the quasi-three-dimensional electron gas with over 5.5 nm spatial distribution ubiquitously exists and shows similar orbital occupations. The signature of electron-phonon coupling is observed and intriguingly dependent on the interfacial orientations. Remarkably, the stronger electron-phonon coupling signature correlates with the higher superconducting transition temperature. Our observations help scrutinize the theories on the orientation-dependent superconductivity and offer a plausible and straightforward explanation. The interfacial orientation effect that can modify the electron-phonon coupling strength over several nanometers sheds light on the applications of oxide interfaces in general.