Is the population of close-in planets orbiting M dwarfs sculpted by thermally driven escape or is it a direct outcome of the planet formation process? A number of recent empirical results strongly suggest the latter. However, the unique architecture of the TOI-1266 system presents a challenge to models of planet formation and atmospheric escape given its seemingly 'inverted' architecture of a large sub-Neptune (Pb = 10.9 d, $R_{p,b}=2.62\pm 0.11\, \mathrm{R}_{\oplus }$) orbiting interior to that of the system's smaller planet (Pc = 18.8 d, $R_{p,c}=2.13\pm 0.12\, \mathrm{R}_{\oplus }$). Here, we present revised planetary radii based on new TESS and diffuser-assisted ground-based transit observations, and characterize both planetary masses using a set of 145 radial velocity measurements from HARPS-N ($M_{p,b}=4.23\pm 0.69\, \mathrm{M}_{\oplus }, M_{p,c}=2.88\pm 0.80\, \mathrm{M}_{\oplus }$). Our analysis also reveals a third planet candidate (Pd = 32.3 d, $M_{p,d}\sin {i} = 4.59^{+0.96}_{-0.94}\, \mathrm{M}_{\oplus }$), which if real, would form a chain of near 5:3 period ratios, although the system is likely not in a mean motion resonance. Our results indicate that TOI-1266 b and c are among the lowest density sub-Neptunes around M dwarfs and likely exhibit distinct bulk compositions of a gas-enveloped terrestrial (Xenv,b = 5.5 ± 0.7 per cent) and a water-rich world (WMFc = 59 ± 14 per cent), which is supported by hydrodynamic escape models. If distinct bulk compositions are confirmed through atmospheric characterization, the system's unique architecture would represent an interesting test case of inside-out sub-Neptune formation at pebble traps.