what I want to understand:
is it bitcoin mining alone that is using water from the lake to cool its mining equipment and as a consequence the lake water becomes hot or is it the gas plant that is using the lake water to cool its equipment and as a consequence the water of the lake is too hot?
The water is used to cool the power plant equipment and regardless of what the load is (miners or grid), for the same power output the resulting temperatures would be the same. Nowhere is anything said about mining changing the
average temperature of the lake and of course water temps near the plants outflow will be fairly warm. That is a rather important point as the article says "nearby residents are reporting the water is like a hot tub" and nothing about the overall temp. In short: water temps are within licensed norms.
Do keep in mind that the plant was built to be used for load leveling when power demand on the grid is high - think of it as a reserve generating station - and normally is running at reduced power, ready for output to be increased when a large demand is predicted. Thing is, power plants cannot just be throttled up and down willy-nilly, they need to be kept operating within fairly narrow margins with large changes happening over several hours
So, the plant operators had a choice: Accept the costs of normal slow response and wildly varying power plant efficiencies due to it not operating near full power (as has been the only historical choice prior to crypto mining)
OR use (their) miners to provide a solid baseline load so the plant can operate near full power keeping the equipment happy and yet allowing the power plant to very quickly supply reserve power to the grid simply by throttling back on the number of miners running. Once grid demands drop off the miners are restarted and the plants boilers or turbines continue operating in a steady state. Increased plant performance aside, mining of course has the bonus of providing a new direct source of income to the plant operators. In my book it's a win-win for all.
The only down side is that the thermal output into the lake is more constant vs fluctuating up & down as it did prior to crypto mining at the site.