but to develop better intuition, think of the sun's gravity as a field in space and nothing is being dragged anywhere, it's just that wherever you are feels appropriate to where you are and where you are going is the path of least resistance, and the places around you feel the same way, and where you all are in relation to each other (in this field) changes its relative position to everything else.

the water of an incoming tide doesn't feel "i'm being dragged uphill", it feels "hey, the earth is moving underneath me". it's all in freefall all the time.

you don't feel like you are rotating at 1000 mph (1600 kph) but you do feel your weight against the surface of the earth. same with the water, except it feels itself being squeezed by everything around it like you only feel that in the entrance to a crowded venue.

so, the water on the side toward the moon and the water on the side away from the moon would mostly perceive the earth as dropping away or coming closer (if they could perceive anything at all) where they are is always their point of reference