Is it wrong to equate it to energy, if one can deduce how it is "INDIRECTLY" related.
Also, not all efficient miners win the nonce all the time, but I get your point.
Discussion
The point is that hashrate is what's desirable (and directly linked to Bitcoin), not energy use.
If someone improves efficiency such that energy use is decreased while hashrate increases, THAT is desirable.
Of course, in the real world every time efficiency increases, energy usage goes UP, not down, because the efficient use of energy makes it more affordable and thus available to a wider market of users.
But the energy consumption is incidental to the generation of hash, or else we'd all just be firing up the least efficient (but cheapest) miners available in order to consume as much energy as possible, which is obviously not the case.
Even if that was the case, the difficulty would adjust to factor all of those new hash. I believe BTC is emitted right?
I agree with your points, however nuanced they might sound, I think you're correct.
Would you say that hashrate and energy are mutually exclusive?
The difficulty would indeed adjust to factor the new hash - and if you were someone still trying to use more energy on older, less efficient, miners, you'll be left in the dust comparatively, even if you're still consuming more energy than others using the more efficient miners.
Energy and hashrate are definitely NOT unconnected, it's just that they're not connected at a fixed 1:1 ratio. The efficiency of the hashrate production is the abstraction between Bitcoin and the energy used to mine.