Galaxy mergers have long been proposed as a mechanism for funneling gas toward galactic centres, potentially triggering accretion onto supermassive black holes (SMBHs) and igniting active galactic nuclei (AGN). While simulations often support this scenario, observational studies have yielded conflicting results regarding the AGN-merger connection. In this study, we analyze 31 galaxies from cosmological zoom-in simulations spanning redshifts 0.5 < z < 3. We identify mergers using detailed merger trees based on six-dimensional dark matter particle information and identify AGN activity through SMBH accretion histories. To bridge the gap between simulations and observations, we generate mock JWST-like images and extract non-parametric morphological parameters. Employing a k-nearest neighbours (KNN) classifier in a five-dimensional space (four morphological parameters and redshift), we identify mergers in the mock-observed dataset. Our analysis reveals a statistically significant enhancement of AGN activity in merging systems, particularly at lower redshifts (0.5 < z < 0.9), where central gas reservoirs are more depleted. This supports the view that mergers contribute more significantly to AGN triggering in environments with low internal gas reservoirs, while their impact may be less pronounced in gas-rich systems. However, when relying solely on morphological classifications from mock observations, the observed AGN-merger connection weakens, especially at higher redshifts. This underscores the challenges in detecting merger-induced AGN activity observationally and highlights the importance of combining simulations with realistic mock observations to fully understand the AGN-merger relationship.