A correlation test and a simple linear regression test both answer the same question, which is
Is there a good chance that my data comes from a population where the correlation is positive rather than negative / where the regression line has a positive slant rather than negative?
Both are based on the Least Squares method, and output the same p-value. They're basically the same test with a slightly different wording of the interpretation (also apart from the fact that Linear Regression allows you to make predictions which correlation alone can't).
I would therefore expect similar assumptions in both tests. Yet normality of variables is a standard requirement in the correlation test, and is not required in the linear regression test.
Why is that?