Will the dynamic equilibrium between water vapor and its liquid phase be disrupted if the external pressure is increased?

A similar question has already been asked here, but my question will be slightly different. Let’s take a cylindrical glass container. Let’s fill it with water and close it. There will be air above the water in the container. The air exerts pressure on the water. Suppose a dynamic equilibrium has been established in the container between the water and its vapor. If we pump more air into the container, the air pressure inside will increase; the air will begin to exert greater pressure on the water, and the water molecules will predominantly return to the liquid phase rather than escape from it. An increase in external pressure will not increase the number of molecules leaving the liquid. Will the dynamic equilibrium between the liquid and its vapor be disrupted in this case? If not, explain why.