But if you don't define your variables, an equation becomes a bit useless. Was it really that Ohm didn't use the "gate-kept" language or that he didn't actually know what he was talking about?

The pitch-perfect critique would've had to be "You've got some great work, but this bit here is hard to follow or outright inconsistent". Instead, they shouted him out of the profession because of the surety of their convictions.

EMF is a DC voltage present even in an open circuit, when no current is drawn. EMF comes from a cell/battery or DC generator. EMF is the cause; potential difference is the effect.

One aspect I'd noticed is that EMF doesn't necessarily have a corresponding potential difference. Eg. a generator with the output short-circuited still has the same EMF as if it was open circuit but potential difference is zero or near-zero across any two points in its windings or circuit.

As I understand it, an EMF has to come from nonelectrical energy, such as chemical, thermal, mechanical, or electromagnetic energy. So if you are drawing your circuit with a battery, you could call that EMF but if you are drawing it with a generic voltage source, you would not call that EMF per se.

It is much the same as your teachers not being able to bridge the gap between concepts you understand and those needed to understand EMF and PD.

Everything seems so obvious now, but now, we have accurate multimeters, low internal resistance power supplies and color-coded resistors. They didn't have anything like that in the early 1800s.

Gatekeeping is a thing of course, and it certainly didn't help in Ohm's case, but it is easy to forget the context in which discoveries are made. It is a bit like heliocentrism, obvious now, but when the idea was first introduced, it was actually worse than the theories of that time, based on epicycles, it wasn't just obscurantism.