If you categorically disagree with my suggestion to make rank public and move spearman into its own named function, I will accept this (you've done the hard work writing the code and I do like the feature). But I do strongly request that we keep to the design of separate named functions rather than overloading the one function with a flag.

If you categorically want to keep the single correlation function, then we could future-proof it and make the type of correlation more explicit with an enumerated flag rather than a bool:

def correlation(x, y, /, kind='pearson'):
    if kind == 'spearman':
        x = _rank(x)
        y = _rank(y)
   elif kind != 'pearson':
       raise ValueError('unsupported correlation kind')

If we ever add another sort of correlation (say, Kendall tau) is would be awkward to handle a second bool flag.