DOC: Make API reference intro section concise (#19846)

Author: Wilson Lin

doc/source/api.rst

@@ -6,19 +6,18 @@ API Reference
 *************
 
 This page gives an overview of all public pandas objects, functions and
-methods. In general, all classes and functions exposed in the top-level
-``pandas.*`` namespace are regarded as public.
+methods. All classes and functions exposed in ``pandas.*`` namespace are public.
 
-Further some of the subpackages are public, including ``pandas.errors``,
-``pandas.plotting``, and ``pandas.testing``. Certain functions in the
-``pandas.io`` and ``pandas.tseries`` submodules are public as well (those
-mentioned in the documentation). Further, the ``pandas.api.types`` subpackage
-holds some public functions related to data types in pandas.
+Some subpackages are public which include ``pandas.errors``,
+``pandas.plotting``, and ``pandas.testing``. Public functions in
+``pandas.io`` and ``pandas.tseries`` submodules are mentioned in
+the documentation. ``pandas.api.types`` subpackage holds some
+public functions related to data types in pandas.
 
 
 .. warning::
 
-    The ``pandas.core``, ``pandas.compat``, and ``pandas.util`` top-level modules are considered to be PRIVATE. Stability of functionality in those modules in not guaranteed.
+    The ``pandas.core``, ``pandas.compat``, and ``pandas.util`` top-level modules are PRIVATE. Stable functionality in such modules is not guaranteed.
 
 
 .. _api.functions: