Galaxy major mergers are a potential mechanism for triggering active galactic nuclei (AGN) activity, but their role remains debated, particularly beyond the local Universe. We aim to shed light on the merger─AGN connection at z = 0.5─2, exploiting the multi-wavelength datasets and James Webb Space Telescope (JWST) observations in the COSMOS field. We construct a stellar mass-limited sample and identify AGN via mid-infrared (MIR) colours, X-ray detections, and spectral energy distribution (SED) fitting. We train convolutional neural networks to identify mergers with mock JWST observations. We create non-AGN and non-merger control samples matching the redshift, stellar mass, and star formation rate distributions of the AGN and mergers. We find AGN to be somewhat more frequent in mergers than in non-mergers, with excess ratios ranging from ∼2.5 (X-ray AGN) to ∼1.3 (MIR) and ∼1.1─1.2 (SED AGN). Similarly, AGN galaxies show a higher merger fraction (fmerg) than non-AGN controls. We then study fmerg as a function of relative and absolute AGN power, utilising the AGN fraction (fAGN) and accretion disc luminosity (Ldisc) parameters. We uncover a fmerg─fAGN relation with two regimes: fmerg stays roughly flat for less-dominant AGN (fAGN < 0.8) but increases at fAGN > 0.8 for the MIR and X-ray AGN, and more gently for SED AGN, where mergers appear to be the main triggering mechanism. Additionally, fmerg increases monotonically as a function of Ldisc, for all AGN types, reaching fmerg > 50% for the most luminous AGN (Ldisc ≳ 1046 erg s−1). Overall, our results suggest that major mergers can trigger AGN out to cosmic noon at z ∼ 2. Furthermore, the role of major mergers shows a clear dependence on AGN luminosity and remains the principal mechanism for fuelling the most powerful AGN.
