  Two-dimensional electron gases (2DEGs) in SrTiO$_3$ have become model systems
for engineering emergent behaviour in complex transition metal oxides.
Understanding the collective interactions that enable this, however, has thus
far proved elusive. Here we demonstrate that angle-resolved photoemission can
directly image the quasiparticle dynamics of the $d$-electron subband ladder of
this complex-oxide 2DEG. Combined with realistic tight-binding supercell
calculations, we uncover how quantum confinement and inversion symmetry
breaking collectively tune the delicate interplay of charge, spin, orbital, and
lattice degrees of freedom in this system. We reveal how they lead to
pronounced orbital ordering, mediate an orbitally-enhanced Rashba splitting
with complex subband-dependent spin-orbital textures and markedly change the
character of electron-phonon coupling, co-operatively shaping the low-energy
electronic structure of the 2DEG. Our results allow for a unified understanding
of spectroscopic and transport measurements across different classes of
SrTiO$_3$-based 2DEGs, and yield new microscopic insights on their functional
properties.
