I've practiced breath meditation in a way similar to how Ven. Thanissaro teaches for decades.
What he and his teacher Ajahn Lee call breath energy, in the Buddha's sutta terminology, corresponds mostly with wind property (see MN 62 for breath meditation and 4 elements)
but also breath energy would overlap with the other elemental properties (fire, water, earth), just that it's the physical tactile sensations of the breath that you filter your experience through.
For example, in the beginning breath tactile sensations may feel most prominent as wind element in nostril area, force of chest and belly expanding.
The more you meditate, the more sensitive you become, and the more that your internal energies of your jhana battery are charged up and the forces become stronger, then you'll feel portions of currents and loops of energy running all over the entire body, felt as watery hydraulic movement, or heat, or electricity. At different stages, parts of your body may feel light (weight) or heavy, maybe like a buzzing beehive, or soft gooey magnetic force everywhere for example.
The sensations of your fingers for example may be felt as tingly electrical sensations. It may not feel like "breath" at first, but the more your jhana battery gets charged up, the more all of these elemental tactile sensations pervade everywhere in the body and connect together.
The important point is not that all of these kinds of tactile sensations have to feel like a gross (airy) breath, but that you simply use the "breath energy" as a way to anchor your perceptions, gross to subtle of how each cell of the body is perceived.