When electrons oscillate in antenna the do work against resistance which becomes heat so from where it gets energy to create radiation
In general electric circuits need batteries or generators to work. Heat is part of the product , the drifting electrons in the resistances scatter and change the kinetic energy of the lattices, and thus generate heat.
In alternating currents part of the current variation goes to the above described heat, and part to electromagnetic radiation because of the acceleration/deceleration cycle forced on the drifting electrons.
In antennas this radiation is coherent, the radiation from the lattice electrons of the fermi level generating an electromagnetic wave .
In energy conservation all the dissipation sinks have to be added up, from resistances and from radiation.