In fact, causality is the opposite (this applies to the labor theory of value in general). The cost of mining bitcoins is based on their value. If bitcoins increase in value, more people will mine (because mining is profitable), therefore the difficulty will increase and the cost of mining will increase. The opposite happens if bitcoins go down in value. These effects are balanced to make mining always cost an amount proportional to the value of bitcoins it produces.
Here is an explanatory audio (EN) on the energy consumption to mine Bitcoin.
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