That phrase is simply inaccurate. Your "self" needs to care less about opinions of others, and it should not be scared of making mistakes. "Be yourself" is typically parsed as "do not try to be someone other, do not try to be like movie actor".

> not "acting intuitively without overthinking", since the socially anxious person's intuition is to run away.

Yes, it is exactly that, but instead of focusing on "acting intuitively", focus on that "without overthinking". Overthinking is the problem to be solved. "thinking just enough" is the optimal target.