Warm rocky exoplanets within the habitable zone of Sun-like stars are favoured targets for current and future missions. Theory indicates these planets could be wet at formation and remain habitable long enough for life to develop. However, it is unclear to what extent an early ocean on such worlds could influence the response of potential biosignatures. In this work we test the climate-chemistry response, maintenance, and detectability of biosignatures in warm, water-rich atmospheres with Earth biomass fluxes within the framework of the planned LIFE mission. We used the coupled climate-chemistry column model 1D-TERRA to simulate the composition of planetary atmospheres at different distances from the Sun, assuming Earth's planetary parameters and evolution. We increased the incoming instellation by up to 50 percent in steps of 10 percent, corresponding to orbits of 1.00 to 0.82 AU. Simulations were performed with and without modern Earth’s biomass fluxes at the surface. Theoretical emission spectra of all simulations were produced using the GARLIC radiative transfer model. LIFEsim was then used to add noise to and simulate observations of these spectra to assess how biotic and abiotic atmospheres of Earth-like planets can be distinguished. Increasing instellation leads to surface water vapour pressures rising from 0.01 bar (1.31<!PCT!>, S = 1.0) to 0.61 bar (34.72<!PCT!>, S = 1.5). In the biotic scenarios, the ozone layer survives because hydrogen oxide reactions with nitrogen oxides prevent the net ozone chemical sink from increasing. Methane is strongly reduced for instellations that are 20<!PCT!> higher than that of the Earth due to the increased hydrogen oxide abundances and UV fluxes. Synthetic observations with LIFEsim, assuming a 2.0 m aperture and resolving power of a R = 50, show that ozone signatures at 9.6 mu m reliably point to Earth-like biosphere surface fluxes of O$_2$ only for systems within 10 parsecs. The differences in atmospheric temperature structures due to differing H$_2$O profiles also enable observations at 15.0 mu m to reliably identify planets with a CH$_4$ surface flux equal to that of Earth's biosphere. Increasing the aperture to 3.5 m and increasing instrument throughput to 15<!PCT!> increases this range to 22.5 pc.