The energy coupled into the plasma system by external electromagnetic fields is absorbed by charged particles, then transported and converted in space, and finally dissipated through processes such as boundary loss and collisions. In this work, we investigate this complete energy dynamics in capacitively coupled oxygen discharges operating in two typical regimes, namely the α mode and the drift-ambipolar (DA) mode. Using particle-in-cell/Monte Carlo collision (PIC/MCC) simulations together with the first three velocity moments of the Boltzmann equation, we construct the transport equations for the total electron energy and further decomposes it into electron fluid kinetic energy (mechanical energy) and thermal energy (internal energy). The results show that electron energy dynamics differ fundamentally between the two modes. In α mode, electrons mainly absorb energy at the region of the expanding sheath and first gain directed kinetic energy, which is then converted locally into thermal energy through pressure-strain interaction and collisional friction. Since the electron kinetic energy remains largely confined to the sheath region, most of this energy is transported into bulk region in the form of heat flux and is gradually dissipated during this process through electron-neutral inelastic collisions. In DA mode, the enhanced electronegativity strongly modifies the spatial distribution of electron density, causing electron energy absorption to occur mainly in the drift field within the bulk and in the ambipolar field near the edge of the collapsing sheath. Because the pressure-strain effect is weakened in the bulk, the directed kinetic energy gained by electrons is only partly converted into thermal energy through collisional friction. As a result, electrons can convect both kinetic and thermal energy from the bulk toward the opposite sheath, where the energy is eventually dissipated through inelastic collisions. The above difference in energy dynamics originates from the electronegativity-induced reconstruction of the electric-field distribution, which reorganizes the spatial separation of electron energy absorption and loss. This not only alters the dominant pathway of kinetic-to-thermal energy conversion, but also ultimately reverses the direction of the electron energy flux. The present work provide a self-consistent kinetic basis for understanding the electron energy dynamics and their differences in oxygen CCPs in the α and DA modes.