Using angle-resolved photoemission spectroscopy, we show that the recently discovered surface state on SrTiO₃ consists of nondegenerate t_2g states with different dimensional characters. While the d_xy bands have quasi-2D dispersions with weak k_z dependence, the lifted d_xz/d_yz bands show 3D dispersions that differ significantly from bulk expectations and signal that electrons associated with those orbitals permeate the near-surface region. Like their more 2D counterparts, the size and character of the d_xz/d_yz Fermi surface components are essentially the same for different sample preparations. Irradiating SrTiO₃ in ultrahigh vacuum is one method observed so far to induce the "universal" surface metallic state. We reveal that during this process, changes in the oxygen valence band spectral weight that coincide with the emergence of surface conductivity are disproportionate to any change in the total intensity of the O 1s core level spectrum. This signifies that the formation of the metallic surface goes beyond a straightforward chemical doping scenario and occurs in conjunction with profound changes in the initial states and/or spatial distribution of near-E_F electrons in the surface region.