V=IR is derived under the assumption that the current is constant, the potential in this equation is the potential required to maintain a constant current under the influence of a resistive term.
This resistive term is responsible for negative work being done on electrons in the wire. And is also the amount of energy being transfered as Heat.
Ohms law is also derived as a steady state solution. Aka, the amount of work required to actually get a current going initially is negligible, the only amount of energy needed is to overcome those resistive forces
For a constant current to exist. The amount of work that the induced emf is doing, (as a result of macroscopic motion) must be equal to the amount of negative work that the resistive term is doing on electons. This is because there is a net 0 gain of KE for a constant current.
Thus work that is being lost to due the resistive term is thermal motion, aka the energy that s being transfered to the object through collisions with the electrons that make up the current
Because we have equated the amount of work done by the emf and the amount of energy lost as thermal motion, we can the use
to find the rate at which energy is being lost as heat.
As this equation represents the amount of work that is being done on charges in a volume through a potential V. So when we input the potential as V= IR, we know this is going to be the same thing as the energy lost through joule heating.