How “sensitive” is chi-square to detect dependence?

I hope I understand chi-square correctly.

Taking the categorical data in chi-square wikipedia page as an example, https://en.wikipedia.org/wiki/Chi-squared_test

I was wondering how "sensitive" chi-square test is to conclude if the occupations and neighborhoods are dependent or independent.

Does a significant p-value indicate that there is some dependency and does not care where exactly the dependency lies and cannot quantify how much dependency there is ?

For example, would chi-square show a significant p-value (<0.05) if there is no association of occupations and neighborhoods for B,C, and D neighborhoods, but there is an association (dependence) only between A neighborhood and blue collar and no collar, but not with white collar? Or does p <0.05 indicate there is some dependency in this neighborhood and occupation example but does not know where (between which elements in the categories) the dependency is and how much dependency there is between the two categories.