We report the detection of GJ 3090 b (TOI-177.01), a mini-Neptune on a 2.9-day orbit transiting a bright (K = 7.3 mag) M2 dwarf located at 22 pc. The planet was identified by the Transiting Exoplanet Survey Satellite and was confirmed with the High Accuracy Radial velocity Planet Searcher radial velocities. Seeing-limited photometry and speckle imaging rule out nearby eclipsing binaries. Additional transits were observed with the LCOGT, Spitzer, and ExTrA telescopes. We characterise the star to have a mass of 0.519 ± 0.013 M⊙ and a radius of 0.516 ± 0.016 R⊙. We modelled the transit light curves and radial velocity measurements and obtained a planetary mass of 3.34 ± 0.72 ME, a radius of 2.13 ± 0.11 RE, and a mean density of 1.89−0.45+0.52 g cm−3. The low density of the planet implies the presence of volatiles, and its radius and insolation place it immediately above the radius valley at the lower end of the mini-Neptune cluster. A coupled atmospheric and dynamical evolution analysis of the planet is inconsistent with a pure H-He atmosphere and favours a heavy mean molecular weight atmosphere. The transmission spectroscopy metric of 221−46+66 means that GJ 3090 b is the second or third most favorable mini-Neptune after GJ 1214 b whose atmosphere may be characterised. At almost half the mass of GJ 1214 b, GJ 3090 b is an excellent probe of the edge of the transition between super-Earths and mini-Neptunes. We identify an additional signal in the radial velocity data that we attribute to a planet candidate with an orbital period of 13 days and a mass of 17.1−3.2+8.9 ME, whose transits are not detected.