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Active Galactic Nucleus (AGN) feedback plays a critical role in galaxy formation and evolution. AGN-driven winds can significantly influence their host galaxies, although the details of their impact remain unclear. In this study, we investigate the feedback effects of AGN winds on idealized disc galaxies using the SWIFT hydrodynamical code with COLIBRE subgrid physics. We implement a new thermal AGN feedback model in which the energy injection coupling efficiency has a power-law dependence on the Eddington ratio of the black hole (BH) accretion rate, motivated by scaling relations for AGN winds from numerical models and observations. We simulate idealised Milky Way-mass galaxies, incorporating a BH, cold gas disc, stellar disc, and hot circumgalactic medium, within a static dark matter halo. We vary the BH mass and the slope and normalisation of the new coupling efficiency model. For a fixed BH mass, we find that while systematic trends with coupling efficiency exist, most galaxy and BH properties show only modest variations. This likely reflects BH self-regulation in the COLIBRE model, which modulates the effects of changes in the feedback efficiency, provided the BH mass is sufficiently high. Key exceptions are the BH accretion rate and mass growth history, and outflow behaviour, where lower coupling efficiencies lead to faster BH growth and weaker outflows, potentially helping to explain the presence of overmassive BHs at high redshifts. Varying the BH mass, however, has a much larger impact, confirming that BH mass remains the primary factor shaping galaxy and BH evolution in our simulations.