Context. Sub-Neptunes are absent in the Solar System, yet they are the most common category of planets found in our Galaxy. This kind of planet challenges the internal structure models, prompts investigations into its formation and evolution, and pushes atmospheric characterisation studies to break the degeneracy in their inner composition. Aims. We report here the discovery and characterisation of new sub-Neptunes orbiting two similar M dwarfs, TOI-521 (Teff = 3544 ± 100 K, V = 14.7 mag) and TOI-912 (Teff = 3572 ± 100 K, V = 12.7 mag). Each star hosts a transiting planetary candidate identified by TESS and is part of the THIRSTEE follow-up programme, which aims to understand the sub-Neptune population through in-depth and precise characterisation studies on a population level. Methods. We analysed TESS light curves, ground-based photometry, and high-precision ESPRESSO, HARPS, and IRD radial velocities to confirm the planetary nature of both candidates, infer the precise orbital and physical parameters of the planets, and investigate the presence of additional planets in the systems. Results. The two stars host nearly identical planets in terms of mass and radius. TOI-521 hosts a transiting sub-Neptune in a 1.5-day orbit with radius and mass of Rb = 1.98 ± 0.14 R⊕ and Mb = 5.3 ± 1.0 M⊕, respectively. Moreover, we identified an additional candidate at 20.3 days, with a minimum mass of Mp sin i = 10.7−2.4+2.5 M⊕, currently not detected as transiting in our photometric dataset. Similarly, the planet orbiting TOI-912 is a 4.7-d sub-Neptune with Rb = 1.93 ± 0.13 R⊕ and Mb = 5.1 ± 0.5 M⊕. Interestingly, TOI-912 b likely possesses an unusually high eccentricity (e = 0.58 ± 0.02) and is probably undergoing strong tidal dissipation. If such eccentricity were confirmed, it would make TOI-912 b one of the most eccentric sub-Neptunes known to date. TOI-521 b and TOI-912 b have very similar densities (~4 g cm−3), and they lie in the degenerate region of the mass-radius diagram where different compositions are plausible, including a volatile-rich composition, or a rocky core surrounded by a H-He envelope. When compared to the other THIRSTEE M-dwarf targets, our sample supports the division of sub-Neptunes into two distinct populations divided by a density gap. Both planets are interesting targets for atmospheric follow-up in the context of understanding the temperature-atmospheric feature trend that starts to emerge thanks to JWST observations.