The (111) orientation of SrTiO₃ (STO)-based heterostructures has emerged as a versatile platform for two-dimensional electron gases (2DEGs), yet the influence of STO's polar ferroelastic domain-wall (DW) network on charge transport remains largely unexplored. Here we study AlOₓ/STO (111) interfaces hosting 2DEGs of different carrier densities. In the lower-density 2DEG, low-temperature transport exhibits thermal hysteresis, slow resistance relaxation, cooling-rate dependence, and memory effects, signaling glasslike electron dynamics. The relaxation is strongly non-monotonic in temperature, increasing below ∼80 K, peaking near 25 K, and vanishing below ∼12 K, tracking the established evolution of the ferroelastic DW state of bulk STO rather than any electronic energy scale, which identifies the DW network as its origin. These signatures are absent in a second, more metallic interface with much higher carrier density, demonstrating that the electron-DW coupling can be tuned. We further show that polar DWs govern the photoresponse: the persistent photoconductivity rises sharply below ∼80 K, coinciding with the onset of DW polarity. Together, these results establish polar ferroelastic DWs as a carrier-density-tunable electronic degree of freedom in STO (111)-based 2DEGs, opening routes to manipulate 2DEG properties through topological defects.