Who was first to ask when our sun might exhaust itself?

Another one of THOSE questions based on an absence of basic understanding. Nothing could be more vague than the term “modern scientific understanding”. Considering that the composition and functioning of the sun has been understood for less than a hundred years, Newton is out of the picture. The pieces to the puzzle were parsed and assembled back in the 1920s & 30s. Newton could approximate the mass of the sun, but its composition had to await advancement in spectography. So you have the fuel and quantity of fuel, but it’s useless until you can explain the rate at which the fuel is “burned” requiring an explanation as to HOW the fuel is burned. So when was the concept of nuclear fusion established?

I’m not sure anyone pondered the question as such. More of a realization once we started learning more about stars, their composition, their various phases, etc.

Here is a snipped from a 1863 article

“If the sun were composed of coal, it would last at the present rate only 5,000 years. The sun, in all probability, is not a burning, but an incandescent, body. Its light is rather that of a glowing molten metal than that of a burning furnace. But it is impossible that the sun should constantly be giving out heat, without either losing heat or being supplied with new fuel. Assuming that the heat of the sun has been kept up by meteoric bodies falling into it, it is possible from the mass of the solar system to determine approximately the period during which the sun has shone. The limits lie between 100 millions and 400 millions of years.”

HG Wells imagined what the death of the sun would be like in his story “The Time Machine” published 1895.