DOC: remove private parameters from method/constructor signatures
- [x] closes #52028
- [ ] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.


The documentation (e.g. for Series constructor) contain the parameters which are used only internally (fastpath in case of Series). Now if a parameter is private and prefixed with an underscore `_` it will not be part of the signature in the output.

@phofl thanks for the review. Is there any guide on how we do the deprecation? You should start by opening an issue to discuss it Created #52028 for the discussion. Seems like the issue needs more discussion before moving forward with a PR so closing for now, but we can reopen when theres more consensus