Could the Casimir force be just gravity’s behavior on small scales?

This is not possible because then the Casimir force would depend on the distance of the plates and their mass. But that is not what happens since the Casimir effect depends on the material of the plates, their dielectric and conductive properties and their geometry.

So far these correlations are well explained by the fact that macroscopic interfaces change the vacuum expectation value between the two plates, causing a negative pressure.