REF: Split up parsers into smaller files
- [x] closes #38930
- [x] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing.html#code-standards) for how to run them


Refactored them into 4 files, similar to described in the issue. If this is accepted I will try to clean this up a bit more through unifying the calls a bit
