refactor: move public types to comfy_api, eager provider snapshot

Address review feedback:
- Move CacheProvider/CacheContext/CacheValue definitions to
  comfy_api/latest/_caching.py (source of truth for public API)
- comfy_execution/cache_provider.py re-exports types from there
- Build _providers_snapshot eagerly on register/unregister instead
  of lazy memoization in _get_cache_providers

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

comfy_api/latest/__init__.py

@@ -135,11 +135,10 @@ class Caching:
 
         Caching.register_provider(MyCacheProvider())
     """
-    # Import from comfy_execution.cache_provider (source of truth)
+    # Public types — defined in comfy_api.latest._caching (source of truth)
+    from ._caching import CacheProvider, CacheContext, CacheValue
+    # Registry functions — implementation in comfy_execution
     from comfy_execution.cache_provider import (
-        CacheProvider,
-        CacheContext,
-        CacheValue,
         register_cache_provider as register_provider,
         unregister_cache_provider as unregister_provider,
     )

comfy_api/latest/_caching.py

@@ -0,0 +1,43 @@
+from abc import ABC, abstractmethod
+from typing import Optional
+from dataclasses import dataclass
+
+
+@dataclass
+class CacheContext:
+    prompt_id: str
+    node_id: str
+    class_type: str
+    cache_key_hash: str  # SHA256 hex digest
+
+
+@dataclass
+class CacheValue:
+    outputs: list
+    ui: dict = None
+
+
+class CacheProvider(ABC):
+    """Abstract base class for external cache providers.
+    Exceptions from provider methods are caught by the caller and never break execution.
+    """
+
+    @abstractmethod
+    async def on_lookup(self, context: CacheContext) -> Optional[CacheValue]:
+        """Called on local cache miss. Return CacheValue if found, None otherwise."""
+        pass
+
+    @abstractmethod
+    async def on_store(self, context: CacheContext, value: CacheValue) -> None:
+        """Called after local store. Dispatched via asyncio.create_task."""
+        pass
+
+    def should_cache(self, context: CacheContext, value: Optional[CacheValue] = None) -> bool:
+        """Return False to skip external caching for this node. Default: True."""
+        return True
+
+    def on_prompt_start(self, prompt_id: str) -> None:
+        pass
+
+    def on_prompt_end(self, prompt_id: str) -> None:
+        pass