Improve event manager API documentation (#14122)

doc/extdev/event_callbacks.rst

@@ -7,7 +7,7 @@ Connecting callback functions to events is a simple way to extend Sphinx,
 by hooking into the build process at various points.
 
 Use :meth:`.Sphinx.connect` in an extension's ``setup`` function,
-or a ``setup`` function in your projects :file:`conf.py`,
+or a ``setup`` function in your project's :file:`conf.py`,
 to connect functions to the events:
 
 .. code-block:: python
@@ -22,7 +22,7 @@ to connect functions to the events:
 
    Extensions can add their own events by using :meth:`.Sphinx.add_event`,
    and calling them them with
-   :meth:`.Sphinx.emit` or :meth:`.Sphinx.emit_firstresult`.
+   :meth:`.EventManager.emit` or :meth:`.EventManager.emit_firstresult`.
 
 Core events overview
 --------------------