Transactions or not, the higher the price, the dirtier the proof of work blockchain is. Just look at the most recent block: https://www.blockchain.com/btc/block/00000000000000000002865...
reward: 6.25BTC
fees for transactions: 0.5BTC
total revenue: 6.75BTC, that is ~ $350K at the moment.
Each block is mined every 10min on average, so it is 2.1M per hour. So the total energy consumption is limited to $2.1M per hour or $1.5B per month at this price. It would be $150M if the price was $5k instead and $30B if the price goes to $1M per BTC. When that happens, 1 transaction will amount to the energy consumption of an American family for 1 year or more. At $1M per BTC, $360,000,000,000 worth of energy would be wasted per year on calculating a hash of a block that is functionally exactly the same with the same amount of transaction as the one calculated for $360, $3.6 or $0.03.
I'm sure I'm missing something like investors betting on price increases, infrastructure elasticity etc. but the correlation must be roughly like that.