Prompt caching does not work when connecting to third-party agents

### Checked other resources - [x] This is a bug, not a usage question. - [x] I added a clear and descriptive title that summarizes this issue. - [x] I used the GitHub search to find a similar question and didn't find it. - [x] I am sure that this is a bug in LangChain rather than my code. - [x] The bug is not resolved by updating to the latest stable version of LangChain (or the specific integration package). - [x] This is not related to the langchain-community package. - [x] I posted a self-contained, minimal, reproducible example. A maintainer can copy it and run it AS IS. ### Package (Required) - [ ] langchain - [ ] langchain-openai - [x] langchain-anthropic - [ ] langchain-classic - [ ] langchain-core - [ ] langchain-model-profiles - [ ] langchain-tests - [ ] langchain-text-splitters - [ ] langchain-chroma - [ ] langchain-deepseek - [ ] langchain-exa - [ ] langchain-fireworks - [ ] langchain-groq - [ ] langchain-huggingface - [ ] langchain-mistralai - [ ] langchain-nomic - [ ] langchain-ollama - [ ] langchain-perplexity - [ ] langchain-qdrant - [ ] langchain-xai - [ ] Other / not sure / general ### Related Issues / PRs _No response_ ### Reproduction Steps / Example Code (Python) ```python from langchain_anthropic import ChatAnthropic from langchain_core.messages import SystemMessage, HumanMessage model = ChatAnthropic( model_name="claude-opus-4-6", temperature=1, api_key="sk-ant-xxx", base_url="https://code.newcli.com/claude/droid", default_headers={ "User-Agent": "Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/144.0.0.0 Safari/537.36", "anthropic-beta": "prompt-caching-2024-07-31" }, ) system_message = SystemMessage( content=[ { "type": "text", "text": "You are a technology expert." }, { "type": "text", "text": "foo" * 1000, "cache_control": {"type": "ephemeral"} } ], ) human_…