[DOCS] Update API reference (#22911)

Updating API reference with ``openvino`` namespace redesign changes.
This PR addresses the following ticket: 117329

docs/openvino_sphinx_theme/openvino_sphinx_theme/templates/custom-module-template.rst

@@ -1,7 +1,7 @@
 {{ fullname | escape | underline}}
 
 .. automodule:: {{ fullname }}
-  
+
 {% block attributes %}
 {% if attributes %}
    .. rubric:: Module Attributes
@@ -21,7 +21,9 @@
    .. autosummary::
       :toctree:
    {% for func in functions %}
-      {{ func }}
+      {% if not func.startswith('_') %}
+         {{ func }}
+      {% endif %}
    {%- endfor %}
 {% endif %}
 {% endblock %}

docs/sphinx_setup/api/ie_python_api/api.rst

@@ -5,6 +5,12 @@ OpenVINO Python API
    :description: Explore Python API and implementation of its features in Intel® Distribution of OpenVINO™ Toolkit.
 
 
+.. autosummary::
+   :toctree: _autosummary
+   :template: custom-module-template.rst
+
+   openvino
+
 .. autosummary::
    :toctree: _autosummary
    :template: custom-module-template.rst