Not sure If I am understanding your question. Although circuit theory is a simplified model whose function is more centered on providing practical applications, utility and safety. Most of the times the fields are not really necessary.

Notice that the potential has no absolute value. We call it with different names such as tension, voltage or potential difference. The latter is the ones physicist prefers. Technically speaking potential is not a scalar but an increment (or a difference). We say potential U = U1-U0. When we say, potential is let's say 8 V it could be either 18 - 10 or -34 - (- 42) or anything. We need a measurement point. You should ask yourself from where I am I measuring a reference? That's the reason you oftentimes see the ground symbol in circuit theory, it's like let's measure all the differences from this point at 0 volts, so if some place has 9 V is because 9 - 0 = 9 volts.

So every time you are measuring a transient on a oscilloscope you need place your probes, the oscilloscope shows the difference between the two proves in a graphical way.

I have also heard arguments that voltage is how much energy per unit charge a charged particle gains/loses moving through a force field, but again, if the field isn't conservative, this would change based on the path taken through the field...it

Work is based on the path, you can't compare voltage (potential difference) with energy.