fix: follow ProxiedSingleton pattern for Caching class

Add Caching as a nested class inside ComfyAPI_latest inheriting from
ProxiedSingleton with async instance methods, matching the Execution
and NodeReplacement patterns. Retains standalone Caching class for
direct import convenience.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

comfy_api/latest/__init__.py

@@ -25,6 +25,7 @@ class ComfyAPI_latest(ComfyAPIBase):
         super().__init__()
         self.node_replacement = self.NodeReplacement()
         self.execution = self.Execution()
+        self.caching = self.Caching()
 
     class NodeReplacement(ProxiedSingleton):
         async def register(self, node_replace: io.NodeReplace) -> None:
@@ -84,6 +85,20 @@ class ComfyAPI_latest(ComfyAPIBase):
                 image=to_display,
             )
 
+    class Caching(ProxiedSingleton):
+        """External cache provider API for sharing cached node outputs."""
+        from ._caching import CacheProvider, CacheContext, CacheValue
+
+        async def register_provider(self, provider: "ComfyAPI_latest.Caching.CacheProvider") -> None:
+            """Register an external cache provider."""
+            from comfy_execution.cache_provider import register_cache_provider
+            register_cache_provider(provider)
+
+        async def unregister_provider(self, provider: "ComfyAPI_latest.Caching.CacheProvider") -> None:
+            """Unregister an external cache provider."""
+            from comfy_execution.cache_provider import unregister_cache_provider
+            unregister_cache_provider(provider)
+
 class ComfyExtension(ABC):
     async def on_load(self) -> None:
         """