[SPARK-47851][CONNECT][DOCS] Document pyspark-connect package

### What changes were proposed in this pull request?

This PR proposes to document the installation for `pyspark-connect` package

### Why are the changes needed?

So the end users can install pure Python library.

### Does this PR introduce _any_ user-facing change?

Yes, it documents `pyspark-connect` package, and links the quickstart as well.

### How was this patch tested?

Manually built the docs and checked:

```bash
cd python/docs
make clean html
open build/html/index.html
```

### Was this patch authored or co-authored using generative AI tooling?

No.

Closes apache#46054 from HyukjinKwon/SPARK-47851.

Authored-by: Hyukjin Kwon <[email protected]>
Signed-off-by: Hyukjin Kwon <[email protected]>

python/docs/source/getting_started/install.rst

@@ -36,7 +36,7 @@ Python 3.8 and above.
 Using PyPI
 ----------
 
-PySpark installation using `PyPI <https://pypi.org/project/pyspark/>`_ is as follows:
+PySpark installation using `PyPI (pyspark) <https://pypi.org/project/pyspark/>`_ is as follows:
 
 .. code-block:: bash
 
@@ -81,6 +81,19 @@ Supported values in ``PYSPARK_HADOOP_VERSION`` are:
 Note that this installation of PySpark with/without a specific Hadoop version is experimental. It can change or be removed between minor releases.
 
 
+Python Spark Connect Client
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The Python Spark Connect client is a pure Python library that does not rely on any non-Python dependencies such as jars and JRE in your environment.
+To install the Python Spark Connect client via `PyPI (pyspark-connect) <https://pypi.org/project/pyspark-connect/>`_, execute the following command:
+
+.. code-block:: bash
+
+    pip install pyspark-connect
+
+See also `Quickstart: Spark Connect <quickstart_connect.html>`_ for how to use it.
+
+
 Using Conda
 -----------