Anomalies in past neutrino measurements have led to the discovery that these particles have non-zero mass and oscillate between their three flavors when they propagate. In the 2010's, similar anomalies observed in the antineutrino spectra emitted by nuclear reactors have triggered the hypothesis of the existence of a supplementary neutrino state that would be sterile i.e. not interacting via the weak interaction. The STEREO experiment was designed to study this scientific case that would potentially extend the Standard Model of Particle Physics. Here we present a complete study based on our full set of data with significantly improved sensitivity. Installed at the ILL (Institut Laue Langevin) research reactor, STEREO has accurately measured...