Here is the connection: as the price increases, miners put more hashing power on the network, the difficulty rises, which increases the computational power required to mine a block. computational power consumes electrical power. QED BTC price is connected to energy consumption. As this scales, it becomes a factor of consideration in environmentally sustainable operation.
This does not necessarily hold true, though. There is not a direct correlation between hash rate, price, and/or mining reward.
At the end of 2017, hashrate was around 14EH/s, price was $20k, and so block reward was $250,000 + fees.
At the end of 2018, hashrate had increased by three times and was around 40EH/s, but price had fallen by 80% to under $4k and block reward to $45k + fees.
Now, hashrate is at an all time high of 140EH/s, but with the halving, the block reward is $150,000 + fees.
So comparing today to 2017, hashrate is 10 times higher despite the total block reward in fiat being around half of what it was then.
Yes! you are right. I wouldn't be surprised that other factors are apart of the equation, but that is a fair deviation from the base relationship between price and hashrate.
One extra factor from the top of my head is that mining rigs have become more efficient, therefore we are able to get more EH/KWh. The fact that miners have the choice to withhold their coins from the market in anticipation of a bull run is also a factor that makes things very non-linear.