It’s more like gasoline in the sense that it’s in chemical form and the energy is potential. Anyway there is ‘energy’ in the physics sense of ‘the ability to do work’ and then there is energy in the sense of “not made of mass” - these are two different things.
But even in the second case, E=MC^2 so all energy has a mass equivalence. If you had enough energy in the form of light beams bouncing around inside you, you would weigh more on the scale.
And the pure substance mass of the food you are eating is so large in comparison to the increase of potential energy equivalent mass as to make it effectively negligible. You could have a very heavy food (lead) with very little potential energy and a very light food (sugar) with high potential energy. The problem is that even though the high energy extremely high amounts of energy are of very little mass equivelence, it’s attached to heavy molecules.
That said, I think it’s obvious that at least long term energy storage in humans involves saving up more molecules than you started with. This isn’t fundamentally so, though - theoretically, one could strip all of the potential energy from incoming molecules, add all that energy to the atoms that already exist in your body, and then get rid of then get rid of the consumed atoms. Effectively you would see no increase in mass. Technically there would be a small increase in mass equivelance to the tune of energy divided by the speed of light squared, so a tiny amount barely if at all measurable.
How much (chemical) potential energy a molecule holds is related not to how large it is, but rather to how close it is to filling a particular electron shell.