Recreate water bevel

Here is one way using a Warp Modifier

Your surface must be highly subdivided, it will contain the modifier. In the gif below this is the plane object.

The modifier stack is as follows:

The from and to fields in the warp modifier are the important pieces here.

The modifier pulls from point a to point b, thus creating the effect shown in the gif below. By animating the cube to move toward the empty, as well as the strength parameter of the modifier it exaggerates the effect. This should get you in the direction you are looking for.

You could do something like this - Inset the "water surface" a few times around the edge of the glass (for a classic meniscus), and also scale/inset the circle in the center of the "water" to match the shape of the brush and inset it a few times as well.

Then select the main (midgap) water surface turn on proportional editing, and shrink the edit circle until it's small enough that it only affects the water. Move the selected area down and the rings on the edge of the glass and around the brush will start to curve. Position it where you think looks good, and turn any subsurface modifiers back on.

The final result looks like this (I know the glass and reflections are terrible - I made it super fast):