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Diffusion is typically passive, sometimes (rarely) guided. But actual genome delivery usually requires energy stored in the capsid. For membraneous viruses, it's usually energy stored in the spike/fusion protein, plus some help from the host.

Note: I'm talking about energy stored in the 3D structure, not ATP molecules.

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Where does the energy stored in the 3D structure come from? How does it get infused with said energy?

When the virus is made by the previous cell, as the virus is assembled, it is assembled into what is called a "metastable" state. This is a low, but not lowest energy state, or energy well. Typically the lowest possible energy state requires some additional input of energy to reach (it has to get over a small hump to find the deepest well). That energy often comes from an interaction with a new host.

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