Add TOC object entry support for C domain

This is based on the C++ implementation.

Implements #11424

Author: Cynerd

sphinx/domains/c/__init__.py

@@ -39,7 +39,7 @@
 
     from docutils.nodes import Element, Node, TextElement, system_message
 
-    from sphinx.addnodes import pending_xref
+    from sphinx.addnodes import desc_signature, pending_xref
     from sphinx.application import Sphinx
     from sphinx.builders import Builder
     from sphinx.domains.c._symbol import LookupKey
@@ -309,6 +309,32 @@ def after_content(self) -> None:
         self.env.current_document.c_parent_symbol = self.oldParentSymbol
         self.env.ref_context['c:parent_key'] = self.oldParentKey
 
+    def _object_hierarchy_parts(self, sig_node: desc_signature) -> tuple[str, ...]:
+        last_symbol: Symbol = self.env.current_document.c_last_symbol
+        return tuple(map(str, last_symbol.get_full_nested_name().names))
+
+    def _toc_entry_name(self, sig_node: desc_signature) -> str:
+        if not sig_node.get('_toc_parts'):
+            return ''
+
+        config = self.config
+        objtype = sig_node.parent.get('objtype')
+        if config.add_function_parentheses and (
+            objtype in {'function', 'method'}
+            or (objtype == 'macro' and '(' in sig_node.rawsource)
+        ):
+            parens = '()'
+        else:
+            parens = ''
+        *parents, name = sig_node['_toc_parts']
+        if config.toc_object_entries_show_parents == 'domain':
+            return '::'.join((name + parens,))
+        if config.toc_object_entries_show_parents == 'hide':
+            return name + parens
+        if config.toc_object_entries_show_parents == 'all':
+            return '::'.join([*parents, name + parens])
+        return ''
+
 
 class CMemberObject(CObject):
     object_type = 'member'