[3.13] gh-101100: Fix reference warnings in c-api/init.rst documenting PyGILState_STATE (GH-139572)

(cherry picked from commit d2deb8f)

Co-authored-by: Stan Ulbrych <[email protected]>

Author: StanFromIreland

Doc/c-api/init.rst

@@ -1225,9 +1225,23 @@ code, or when embedding the Python interpreter:
    The :term:`GIL` does not need to be held, but will be held upon returning
    if *tstate* is non-``NULL``.
 
+
 The following functions use thread-local storage, and are not compatible
 with sub-interpreters:
 
+.. c:type:: PyGILState_STATE
+
+   The type of the value returned by :c:func:`PyGILState_Ensure` and passed to
+   :c:func:`PyGILState_Release`.
+
+   .. c:enumerator:: PyGILState_LOCKED
+
+      The GIL was already held when :c:func:`PyGILState_Ensure` was called.
+
+   .. c:enumerator:: PyGILState_UNLOCKED
+
+      The GIL was not held when :c:func:`PyGILState_Ensure` was called.
+
 .. c:function:: PyGILState_STATE PyGILState_Ensure()
 
    Ensure that the current thread is ready to call the Python C API regardless
@@ -1372,11 +1386,11 @@ All of the following functions must be called after :c:func:`Py_Initialize`.
    must be held.
 
    .. versionchanged:: 3.9
-      This function now calls the :c:member:`PyThreadState.on_delete` callback.
+      This function now calls the :c:member:`!PyThreadState.on_delete` callback.
       Previously, that happened in :c:func:`PyThreadState_Delete`.
 
    .. versionchanged:: 3.13
-      The :c:member:`PyThreadState.on_delete` callback was removed.
+      The :c:member:`!PyThreadState.on_delete` callback was removed.
 
 
 .. c:function:: void PyThreadState_Delete(PyThreadState *tstate)

Doc/tools/.nitignore

@@ -4,7 +4,6 @@
 
 Doc/c-api/descriptor.rst
 Doc/c-api/float.rst
-Doc/c-api/init.rst
 Doc/c-api/init_config.rst
 Doc/c-api/intro.rst
 Doc/c-api/module.rst