ENH: regex replace capacities are missing from pd.Categorical.replace()

[oguzhanogreden]

Is your feature request related to a problem?

pd.Categorical doesn't implement regex=, preventing a generalisable solution at #32542.

Describe the solution you'd like

As far as I can tell, the best solution would be an refactor of .replace() methods and logic.

API breaking implications

Describe alternatives you've considered

Parts of the logic from array_algos.replace.replace_regex() can be copied over to pd.Categorical, but that's not desirable. Therefore the suggestion for the refactor.

Additional context

This came up while working with the suggestion here.