### What happened?

When using caching with Anthropic web search, the cache does not store the complete response, i.e., the citations stored in `provider_specific_fields`.

As you can see `res1` below includes the citations, while cached result `res2` does not.

We'd love know if this is a bug, known limitation, or something else.

Thanks! 😊

```python import litellm from litellm.caching.caching import Cache litellm.cache = Cache()

res1 = litellm.completion("claude-sonnet-4-20250514", [{'role':'user','content':'Search the web and tell me very briefly about pears.'}], tools=[{ "type": "web_search_20250305", "name": "web_search", "max_uses": 3}])

res2 = litellm.completion("claude-sonnet-4-20250514", [{'role':'user','content':'Search the web and tell me very briefly about pears.'}], tools=[{ "type": "web_search_20250305", "name": "web_search", "max_uses": 3}]) ```

```python # res1 ModelResponse(id='chatcmpl-be3f7553-8251-497d-bc98-319e1e979edb', created=1753716741, model='claude-sonnet-4-20250514', object='chat.completion', system_fingerprint=None, choices=[Choices(finish_reason='stop', index=0, message=Message(content='Pears are fruits produced and…