I'm trying to understand a DC circuit with only battery and light bulb component. In this scenario, electric potential energy as electrons move from negative to positive terminal is converted to kinetic energy of the electrons. So as they move more, their kinetic energy increases. So, we have an energy transfer because electrons when they move and their kenetic increases, the energy actually can be seen as in "transfering mode".
While this is clear to me, I learned now that there exists poynting vector theorem and we also have it here. While it applies to EM waves, we have it in DC circuit as well and this energy doesn't transfer through wire.
Is this energy($\frac{1}{\mu_r} ExB$) completely different from potential and kinetic energy or is it related to them somehow and would we have this energy even if electrons in a circuit travel with constant speed(though I'm not sure how they'd travel with constant speed since each time potential energy transforms into kinetic energy so kinetic energy must be increasing ?)