How can I darken the left side of the sky more than the right?

Probably no better than any other attempts. The degree of darkening is a personal taste of course.

The top shot is the original. I selected the sky and did a copy/paste and selected the sky again in the new layer. Then used the Graduated Neutral Density filter at about 8 to 10% opacity. And then dragged that from left to right.

If I removed the clouds from the sky selection they would have stayed as they were. But I wanted to leave that work for the OP.

You can always step back a step using the History pallet if you don't get it right and do another swipe of the filter.