GJ 877 is a bright M dwarf in the solar neighborhood with two currently reported nontransiting exoplanets with periods of 9d and 21d, along with an additional unconfirmed signal at 50d. We reanalyzed the system with 101 new HARPS and 12 new ESPRESSO radial velocities (RVs) secured with a cadence to confirm or refute the origin of the 50 d signal. To do so, we searched for signals related to stellar activity in photometric data and spectroscopic indicators. We modeled the stellar activity in the RVs with Gaussian processes (GPs). With the Bayesian analysis, we confirmed a four-planet model, including the two previously known planets at periods of 9.2619+/-0.0005d and 21.784+/-0.004d, as well as two newly confirmed exoplanets: an Earth-mass planet, with a 4.42490+/-0.00014d period and a sub-meter-per-second amplitude, and a super-Earth with a 50.77+/-0.05d period located in the habitable zone (HZ). This super-Earth is the second closest planet in the HZ, after Proxima Cen b. We found an additional signal in a 2:1 resonance with the 4.4d planet at 2.21661+/-0.00010d with an amplitude of 0.37+/-0.09m/s, which could be related to an additional planet. However, other explanations of its origin are also plausible. This signal remains a candidate, as further investigation is required to confirm its true nature. If the signal is caused by a planet, its minimum mass would be half that of Earth. We measured the stellar rotation period with the characteristic periodic timescale of the GP. We found a period of 38.7+/-0.5d, which is consistent with the rotation period determined from photometry and other activity indices.