There is actually research that looks at this. There is no correlation between depression or slow self esteem and sexual permissiveness. There isn’t evidence that casual sex makes anyone unhappy, especially if you control for sociocultural variables, as far as I’m aware.

As for why women have become more unhappy, is it true that this trend has been linear? And for how long exactly? And what alternative explanations are there for this?

What if we are more and more raised to believe that we can be the equals of men and more unhappy with the continued sociocultural barriers to that equality?