Low dimensionality, broken symmetry and easily-modulated carrier concentrations provoke novel electronic phase emergence at oxide interfaces. However, the spatial extent of such reconstructions – i.e. the interfacial “depth” – remains unclear. Examining LaAlO₃/SrTiO₃ heterostructures at previously unexplored carrier densities n_2D ≥ 6.9 × 10¹⁴ cm⁻², we observe a Shubnikov-de Haas effect for small in-plane fields, characteristic of an anisotropic 3D Fermi surface with preferential d_xz,yz orbital occupancy extending over at least 100 nm perpendicular to the interface. Quantum oscillations from the 3D Fermi surface of bulk doped SrTiO₃ emerge simultaneously at higher n_2D. We distinguish three areas in doped perovskite heterostructures: narrow (<20 nm) 2D interfaces housing superconductivity and/or other emergent phases, electronically isotropic regions far (>120 nm) from the interface and new intermediate zones where interfacial proximity renormalises the electronic structure relative to the bulk.