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After Einstein, the kinetic energy of a stationary rock and a missing rock were extremely different (by mc in fact).
What this means in terms of energy (which is just the sum of a bunch of different terms that always stays the same) is that “removing an object” now violates the conservation of energy.
E=mc is very non-specific and at the time it was written: not super helpful.
It merely implies that if matter were to disappear, you’d need a certain amount of some other kind of energy to take its place (wound springs, books higher on shelves, warmer tea, other kind); and in order for new matter to appear, a prescribed amount of energy must also disappear.
Rather than being an actual “thing” in the universe, energy is best thought of as an abstract (there’s no such thing as pure energy).
Energy takes a heck of a lot of forms: kinetic, chemical, electrical, heat, mechanical, light, sound, nuclear, etc. For example, the energy stored in a (not overly) stretched or compressed spring is and the energy of the heat in an object is .
As the weight falls, it turns an agitator that heats the water. He did a few fancy things in 1905, including figuring out a better way of doing mechanics.
In fact, it isn’t obvious that all of these different forms of energy are related at all.
Joule had to do all kinds of goofy experiments to demonstrate that, for example, the sum of gravitational potential energy and thermal energy stays constant.
He had to build a machine that turned the energy of an elevated weight into heat, and then was careful to keep track of exactly how much of the first form of energy was lost and how much of the second was gained.
They can also be forgiven for not noticing the mc term wasn’t important for describing anything they were seeing.
It’s a little like being on a boat at sea; the tiny rises and falls of the surface are obvious, but the huge distance to the bottom is not. Before Einstein, the kinetic energy of a completely stationary rock and a missing rock was the same (zero).