  The impact of winds and jet-inflated bubbles driven by active galactic nuclei
(AGN) are believed to significantly affect the host galaxy's interstellar
medium (ISM) and regulate star formation. To explore this scenario, we perform
a suite of hydrodynamic simulations to model the interaction between turbulent
star-forming clouds and highly pressurised AGN-driven outflows, focusing on the
effects of self-gravity. Our results demonstrate that the cloudlets fragmented
by the wind can become gravitationally bound, significantly increasing their
survival time. While external pressurisation leads to a global collapse of the
clouds in cases of weaker winds ($10^{42}-10^{43}~{\rm erg~s^{-1}}$),
higher-power winds ($10^{44}-10^{45}~{\rm erg~s^{-1}}$) disperse the gas and
cause localised collapse of the cloudlets. We also demonstrate that a kinetic
energy-dominated wind is more efficient in accelerating and dispersing the gas
than a thermal wind with the same power. The interaction can give rise to
multi-phase outflows with velocities ranging from a few 100 to several
1000~${\rm km\,s^{-1}}$. The mass outflow rates are tightly correlated with the
wind power, which we explain by an ablation-based mass-loss model. Moreover,
the velocity dispersion and the virial parameter of the cloud material can
increase by up to one order of magnitude through the effect of the wind. Even
though the wind can suppress or quench star formation for about 1 Myr during
the initial interaction, a substantial number of gravitationally bound dense
cloudlets manage to shield themselves from the wind's influence and
subsequently undergo rapid gravitational collapse, leading to an enhanced star
formation rate (SFR).
