Ohm's law is often motivated by the microscopic relation \begin{align} \vec{j} = \sigma \vec{E} \end{align} From this you can easily derive \begin{align} U = RI \end{align} , given that \begin{align} U = \int_{\text{along the resistor}} \vec{E} \vec{ds} \end{align}
However, there are different definitions of "voltage", for example the "voltage" $U$ used in the circuit analysis for inductors, \begin{align} U = L \frac{d I}{dt} \end{align} uses $U$ to be the difference in the lorentz-gauge scalar potential, and not the line integral of the electric field (which would be 0 in a conducting inductor).
Hence the question:
What is the standard way to deal with this ambiguity of "voltage" when it comes to resistors?
Is it common to enhance Ohm's law to account for the additional electric field that a time varying magnetic field would create?
Or is it instead common to use the definition of "voltage" being a line integral?
Or does one simply not bother, because in the approximation of the lumped element model, resistors are never exposed to time varying magnetic fields / rotational electric fields at all?