  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 LaAlO$_3$/SrTiO$_3$ heterostructures at
previously unexplored carrier densities $n_{2D}\geq6.9\times10^{14}$ 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 SrTiO$_3$ 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.
