The abundance of faint dwarf galaxies is determined by the underlying population of low-mass dark matter (DM) halos and the efficiency of galaxy formation in these systems. Here, we quantify potential galaxy formation and DM constraints from future dwarf satellite galaxy surveys. We generate satellite populations using a suite of Milky Way (MW)–mass cosmological zoom-in simulations and an empirical galaxy–halo connection model, and assess sensitivity to galaxy formation and DM signals when marginalizing over galaxy–halo connection uncertainties. We find that a survey of all satellites around one MW-mass host can constrain a galaxy formation cutoff at peak virial masses of ${{ \mathcal M }}_{50}={10}^{8}\,{M}_{\odot }$ at the 1 σ level; however, a tail toward low ${{ \mathcal M }}_{50}$ prevents a 2 σ measurement. In this scenario, combining hosts with differing bright satellite abundances significantly reduces uncertainties on ${{ \mathcal M }}_{50}$ at the 1 σ level, but the 2 σ tail toward low ${{ \mathcal M }}_{50}$ persists. We project that observations of one (two) complete satellite populations can constrain warm DM models with m _WDM ≈ 10 keV (20 keV). Subhalo mass function (SHMF) suppression can be constrained to ≈70%, 60%, and 50% that in cold dark matter (CDM) at peak virial masses of 10 ^8 , 10 ^9 , and 10 ^10 M _⊙ , respectively; SHMF enhancement constraints are weaker (≈20, 4, and 2 times that in CDM, respectively) due to galaxy–halo connection degeneracies. These results motivate searches for faint dwarf galaxies beyond the MW and indicate that ongoing missions like Euclid and upcoming facilities including the Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope will probe new galaxy formation and DM physics.