Energy exists. Energy can be measured. Your units in the end do not matter. Energy is energy. It is a very real thing. It has nothing to do with philosophy.
But as Richard Feynmann tells us, we really have no idea what energy is.
A philisophical answer.
Realy exists regardless of how we think or talk about it.
Seconds measures change, meters measures distance, mass measures matter.
Energy is a human fabrication. Reality exist regardless of what we call it. We tend to take our words for reality as reality itself. 'The map is not the countryside.
I can't get a bucket of Josues, but I can get a bucket of coal which has energy measured in Joules. I can't get a bucket of kilograms, I can get a bucket of coal with weight in kilograms. I can't get a bucket of meters but I can get a bucket of ibjects that are 1 meter long.
If I say light is red then that means the definition f the red wavelength.
Does wavelength exists? I don't think so. Light or EM radiation exists, wavlength is a term we use to quantify it.