No, time dilation and the effects of gravity do not prove that electromagnetism/energy is gravity or vice versa. Time dilation is a phenomenon that occurs due to the warping of spacetime caused by massive objects like black holes, as described by Einstein's theory of general relativity.
Gravity is one of the fundamental forces in nature, and it is described by the theory of general relativity. It is a force that attracts objects with mass towards each other. Electromagnetism, on the other hand, is a separate fundamental force that governs the interactions of electrically charged particles.
While both gravity and electromagnetism are important forces in the universe, they are distinct and described by different theories. General relativity explains gravity as a curvature of spacetime caused by mass and energy, whereas electromagnetism is described by quantum electrodynamics (QED) and is based on the interaction between electric charges and electromagnetic fields.
It is important to note that there are ongoing efforts in physics to unify the fundamental forces, such as the pursuit of a theory of quantum gravity that aims to reconcile general relativity with quantum mechanics. However, there is no widely accepted theory that definitively unifies gravity and electromagnetism.