Context. The evolution of galaxies is influenced by many physical processes, which may vary depending on their environment. Aims. We combine Hubble Space Telescope (HST) and Multi-Unit Spectroscopic Explorer (MUSE) data of galaxies at 0.25 ≲ z ≲ 1.5 to probe the impact of environment on the size-mass relation, the main sequence (MS) relation, and the Tully-Fisher relation (TFR). Methods. We perform a morpho-kinematics modelling of 593 [O II ] emitters in various environments in the COSMOS area from the MUSE-gAlaxy Groups In Cosmos survey. The HST F814W images are modelled with a bulge-disk decomposition to estimate their bulge-disk ratio, effective radius, and disk inclination. We use the [O II ] λλ 3727, 3729 doublet to extract the galaxies’ ionised gas kinematics maps from the MUSE cubes, and we model those maps for a sample of 146 [O II ] emitters, including bulge and disk components constrained from morphology and a dark matter halo. Results. We find an offset of 0.03 dex (1 σ significant) on the size-mass relation zero point between the field and the large structure sub-samples, with a richness threshold of N = 10 to separate between small and large structures, and of 0.06 dex (2 σ ) with N = 20. Similarly, we find a 0.1 dex (2 σ ) difference on the MS relation with N = 10 and 0.15 dex (3 σ ) with N = 20. These results suggest that galaxies in massive structures are smaller by 14% and have star formation rates reduced by a factor of 1.3 − 1.5 with respect to field galaxies at z ≈ 0.7. Finally, we do not find any impact of the environment on the TFR, except when using N = 20 with an offset of 0.04 dex (1 σ ). We discard the effect of quenching for the largest structures, which would lead to an offset in the opposite direction. We find that, at z ≈ 0.7, if quenching impacts the mass budget of galaxies in structures, these galaxies would have been affected quite recently and for roughly 0.7 − 1.5 Gyr. This result holds when including the gas mass but vanishes once we include the asymmetric drift correction.