Studies of close-in planets orbiting M dwarfs have suggested that the M-dwarf radius valley may be well explained by distinct formation timescales between enveloped terrestrials and rocky planets that form at late times in a gas-depleted environment. This scenario is at odds with the picture that close-in rocky planets form with a primordial gaseous envelope that is subsequently stripped away by some thermally driven mass-loss process. These two physical scenarios make unique predictions of the rocky/enveloped transition's dependence on orbital separation such that studying the compositions of planets within the M-dwarf radius valley may be able to establish the dominant physics. Here, we present the discovery of one such keystone planet: the ultra-short-period planet TOI-1634 b (P = 0.989 days, <?CDATA $F=121{F}_{\oplus }$?> , <?CDATA ${r}_{p}={1.790}_{-0.081}^{+0.080}$?> R⊕) orbiting a nearby M2 dwarf (Ks = 8.7, Rs = 0.450 R⊙, Ms = 0.502 M⊙) and whose size and orbital period sit within the M-dwarf radius valley. We confirm the TESS-discovered planet candidate using extensive ground-based follow-up campaigns, including a set of 32 precise radial velocity measurements from HARPS-N. We measure a planetary mass of <?CDATA ${4.91}_{-0.70}^{+0.68}$?> M⊕, which makes TOI-1634 b inconsistent with an Earth-like composition at <?CDATA $5.9\sigma $?> and thus requires either an extended gaseous envelope, a large volatile-rich layer, or a rocky composition that is not dominated by iron and silicates to explain its mass and radius. The discovery that the bulk composition of TOI-1634 b is inconsistent with that of Earth supports the gas-depleted formation mechanism to explain the emergence of the radius valley around M dwarfs with <?CDATA ${M}_{s}\lesssim 0.5$?> M⊙.