Question on William's method (Steiger Test)

I am new to the forum, so first, a big hello to all!

I have a question about William's method (comparison of correlation coefficients). I am running it in R with the 'psych' package. I can confidently compare correlation coefficients with each other and that is really cool for a baby R user like me.

I read the initial paper by Williams, and I vaguely understood the math, but he refers to regression coefficients and not correlation coefficients. In psych literature, however, I have come across the William's method and its modification, the Steiger Test, exclusively for correlation coefficients.

I would like to know if, using the William's method ('r.test' command in the 'psych' package), I can also compare regression coefficients (b) with eachother, and if yes, can I also compare indirect effects of mediations with eachother? (since they are essentially b regression coefficients)

Furthermore, can I extend the use of the William's method to Spearman correlation coefficients as well, or is it appropriate only for Pearson coefficients?

Thank you!
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