[Python][Docs] Revise Python Documentation

### Describe the enhancement requested

This is the umbrella ticket for ongoing efforts to improve and revise the PyArrow Python User Guide and API reference [documentation](https://arrow.apache.org/docs/developers/guide/documentation.html#where-to-find-the-correct-file-to-change).

Many sections of the guide need refreshing, especially based on what users frequently search for and the kinds of issues commonly reported. We’ve already started prioritizing topics through [research](https://colab.research.google.com/drive/1xWUgArhdL6O2ApWHLX6gAy_fzhImmnHv?usp=sharing) using Matomo web analytics and GitHub issues. In the future, insights from Kapa AI will also be incorporated. Comments on the priorities are welcome!

We’ll open sub-issues for specific tasks as we go. Everyone is welcome to contribute—whether you're experienced or just getting started, your help in making the PyArrow docs better is appreciated! ❤️

## Suggested Focus Areas (in order of priority):

1. Parquet module
2. Dataset module
3. `Table`, `RecordBatch`, `Schema` and data types
4. [Getting Started ](https://arrow.apache.org/docs/python/getstarted.html)
5. [Pandas integration](https://arrow.apache.org/docs/python/pandas.html)
6. IPC

_Note:_ The User Guide is the main focus of this revision effort, but improving the API reference documentation is also important. Analytics show it receives a significant amount of traffic, so we'll consider enhancements there as well.

## Existing Documentation Issues

- Datasets
- https://github.com/apache/arrow/issues/29417
- https://github.com/apache/arrow/issues/24261
- https://github.com/apache/arrow/issues/48279
- https://github.com/apache/arrow/issues/41666
- https://github.com/apache/arrow/issues/41496
- https://github.com/apache/arrow/issues/43352

## Connected

- https://github.com/apache/arrow/issues/30021
- https://github.com/apache/arrow/issues/28859

## Extras

- make sure pandas examples are used only in places, where pyarrow integration with pandas is explained.

### Component(s)

Documentation, Python