I am Mario, writing from Germany, I try to spend some time having fun with this wonderful software.
I can't wrap my head around how this effect was obtained:
it comes straight from a Kurzgesagt video (I know, I know, it's probably top tier animation).
I really can't make up an idea on how to deform just some spots of the grid, let alone move this dip around.
Does someone know how it could be done, if at all it can be done in AE?
Since there's no perspective, an animated displacement map is a viable option -- not that it is necessarily easy to figure out what the displacement map should look like, but once you have one figured out for a single "dip", you can copy it, scale it, change opacity and move it around to create the gravity warping effects.. Also, it would need a separate layer for anything that peeks down from the underside. 16 bits for smooth displacement.