feature #58141: Consistent naming conventions for string dtype aliases
Key implementation steps:
- Created factory functions (string, datetime, integer, floating, decimal, boolean, list, categorical, interval, period, sparse, date, duration, map, struct) to generate pandas dtypes (e.g., StringDtype, Int64Dtype, ArrowDtype) based on parameters like backend, bits, unit, and precision.
- Added support for Pandas, NumPy and PyArrow backends, enabling seamless switching (e.g., integer() returns Int64Dtype for Pandas or ArrowDtype(pa.int64()) for PyArrow).
- Implemented parameter validation to ensure correct usage (e.g., validating mode in string() to be "string" or "binary", and unit in datetime() for NumPy).
- Integrated PyArrow types for advanced dtypes (e.g., pa.float64(), pa.list_(), pa.map_()), supporting modern data processing frameworks.
- Implemented comprehensive tests in test_factory.py to validate dtype creation across all functions, ensuring correct behavior for different backends, verifying string representations (e.g., "double[pyarrow]" for pa.float64()), and confirming proper error handling (e.g., raising ValueError for invalid inputs).
- Addressed PyArrow compatibility by implementing correct method calls, such as using pa.bool_() for boolean dtypes, ensuring proper integration.

This change simplifies dtype creation, reduces duplication, and ensures compatibility across backends, making it easier to extend support for new dtypes in the future.

- [x] closes #58141 
- [x] [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).
- [x] 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/v3.0.0.rst` file if fixing a bug or adding a new feature.

@simonjayhawkins Hi! Just wanted to check if this PR needs anything else from my side. Thanks in advance for reviewing This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this.