Decl styling, use a post-transform to get the domain name in the desc_signature nodes

sphinx/addnodes.py

@@ -158,8 +158,9 @@ class desc_signature(_desc_classes_injector, nodes.Part, nodes.Inline, nodes.Tex
     Set ``is_multiline = True`` to describe a multi-line signature.
     In that case all child nodes must be :py:class:`desc_signature_line` nodes.
 
-    This node always has the classes ``sig`` and ``sig-object``.
+    This node always has the classes ``sig``, ``sig-object``, and the domain it belongs to.
     """
+    # Note: the domain name is being added through a post-transform DescSigAddDomainAsClass
     classes = ['sig', 'sig-object']
 
     @property

sphinx/transforms/post_transforms/__init__.py

@@ -232,10 +232,20 @@ class SigElementFallbackTransform(SphinxPostTransform):
             node.replace_self(newnode)
 
 
+class DescSigAddDomainAsClass(SphinxPostTransform):
+    """Add the domain name of the parent node as a class in each desc_signature node."""
+    default_priority = 200
+
+    def run(self, **kwargs: Any) -> None:
+        for node in self.document.traverse(addnodes.desc_signature):
+            node['classes'].append(node.parent['domain'])
+
+
 def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_post_transform(ReferencesResolver)
     app.add_post_transform(OnlyNodeTransform)
     app.add_post_transform(SigElementFallbackTransform)
+    app.add_post_transform(DescSigAddDomainAsClass)
 
     return {
         'version': 'builtin',