Mechanisms Affecting Galaxies Nearby and Environmental Trends (MAGNET)

[ABRIDGED] Galaxy evolution is shaped by internal and external mechanisms that regulate the baryon cycle and star formation activity. We present a theoretical framework based on the GAlaxy Evolution and Assembly (GAEA) semi-analytic model. We extracted portions of simulated volumes that include isolated galaxies, pairs, group, and filament members at z ~ 0, specifically avoiding massive clusters. Galaxies were classified using both intrinsic (halo-based) and observational (2D projected) parameterizations, reconstructing their environmental histories from z = 2 and identifying mergers, tidal interactions, ram pressure stripping (RPS), and starvation. 2D information decreases isolated and group fractions while doubles pairs. More than half of galaxies remain unaffected by the investigated processes since z = 2. Among affected galaxies, mergers dominate at high stellar masses (40-60% at log(M*/Msun) > 10.5). Tidal interactions are less frequent, and their incidence increases with stellar mass. RPS dominates in groups and filaments at intermediate masses (~50%), while starvation ranges from 20 to 30%. The incidence of the different mechanisms depends strongly on both mass and environment, though their imprints on global properties are often subtle. Distinct evolutionary pathways emerge: log(M*/Msun) < 9.5, galaxies in groups and filaments have a faster mass growth than galaxies in the other environments, especially those undergoing starvation, mergers and, to less extent, RPS. Differences are reduced moving to higher masses, where no clear dependence on physical mechanism emerge, even though at these masses a clear star formation suppression is evident in mergers and starved galaxies. This theoretical investigation provides essential context for the recently started multi-wavelength program Mechanisms Affecting Galaxies Nearby and Environmental Trends (MAGNET), which we introduce here.