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 is when.