Not directly related but not "somewhat" correlated either, it's deeply correlated exactly due to profitability, a point you actually mention but somehow don't consider a deep correlation.

Mining profitability is subject to conditions besides the price of a Bitcoin, for example: energy prices, block reward changes, regulation, hardware availability and pricing, etc.

It's really not as simple as hash rate = price. It's more so that they are correlated in direction of change.

Truth. Parent comment is deeply misinformed. BTC already has more than enough hash rate, and it is entirely independent of price.

That does not make sense.

The whole point of proof of work is that it is proof that someone has spent the value in electricity validating a block.

As the price of bitcoin rises, naturally more and more miners will beef up their rigs (that is, spend more money in infrastructure and electricity) to mine BTC, because the rewards and fees are worth more. Note if they didn't do this, anyone could easily have a "free money" arbitrage play, and basic economics says that discrepancy in prices (i.e. the value of a BTC on the market and the cost to mine one) must be arbitraged away.

Think of it this way, if hash rate is independent of price, why does it take the electricity output of Argentina to run the network? It certainly didn't take that much years ago. The reason being that as BTC becomes more valuable there is more reward and thus more competition for miners to mine. As that happens, the hash rate will rise as more power is added to the network.