Fix #126896: Shape Key Editor can't browse actions

The new Action selector (51fd355c01) avoids the need to use
`space_data.action` in the dope sheet (that attribute was a bit of a
hack; the new Action selector was made to avoid that). It failed to take
the dope sheet's shape key mode into account properly, though. This is
now fixed.

Pull Request: https://projects.blender.org/blender/blender/pulls/127177

scripts/startup/bl_ui/space_dopesheet.py

@@ -306,20 +306,24 @@ class DOPESHEET_HT_editor_buttons:
             panel="DOPESHEET_PT_proportional_edit",
         )
 
-    @staticmethod
-    def _draw_action_selector(context, layout):
-        layout.template_action(context.object, new="action.new", unlink="action.unlink")
+    @classmethod
+    def _draw_action_selector(cls, context, layout):
+        animated_id = cls._get_animated_id(context)
+        if not animated_id:
+            return
+
+        layout.template_action(animated_id, new="action.new", unlink="action.unlink")
 
         if not context.preferences.experimental.use_animation_baklava:
             return
 
-        adt = context.object and context.object.animation_data
+        adt = animated_id and animated_id.animation_data
         if not adt or not adt.action or not adt.action.is_action_layered:
             return
 
         # Store the animated ID in the context, so that the new/unlink operators
         # have access to it.
-        layout.context_pointer_set("animated_id", context.object)
+        layout.context_pointer_set("animated_id", animated_id)
         layout.template_search(
             adt, "action_slot",
             adt, "action_slots",
@@ -327,6 +331,18 @@ class DOPESHEET_HT_editor_buttons:
             unlink="anim.slot_unassign_from_id",
         )
 
+    @staticmethod
+    def _get_animated_id(context):
+        st = context.space_data
+        match st.mode:
+            case 'ACTION':
+                return context.object
+            case 'SHAPEKEY':
+                return context.object.data and context.object.data.shape_keys
+            case _:
+                print("Dope Sheet mode '{}' not expected to have an Action selector".format(st.mode))
+                return context.object
+
 
 class DOPESHEET_PT_snapping(Panel):
     bl_space_type = 'DOPESHEET_EDITOR'