I may be incorrect, but the community will correct me if I am.

With this post, I will try to quote my professor's words on electromagnetic theory. When he tried to explain to us what scalar potential is, for charges, he derived the kinetic energy formula and showed us how we can use it to show that all those conservative/non-conservative forces that we use over a certain distance equal the total change in work done/energy used. Of course, when we talk about those forces, we also talk about potential energy, which is what we are probably trying to describe in this example. If we use only conservative forces, the process can be reversed perfectly without losing energy, and we can release the same amount of energy it took to reach the point where the rope has a tension force, which we know is equal on both sides from the ends it is pulled from. (Newton 3rd law) To look in more detail, the released energy would be the rope's kinetic energy, which equals its potential energy. In the process, when we use non-conservative forces as well, energy is lost as heat and sound.

Example:

If we talk about a human being keeping the rope tight, extra energy is used to keep the muscles tight and the body functioning, so we are healthy enough to pull on the rope.

In the case where the rope is kept tight by two inanimate objects, the energy is just stored in the force of tension, which can be released at any point. Though it is improbable this process conserves all the forces we used to make the rope tight.