Feature: Add Responses API support to ChatOpenRouter (use_responses_api=True)

### Submission checklist - [x] This is a feature request, not a bug report or usage question. - [x] I added a clear and descriptive title that summarizes the feature request. - [x] I used the GitHub search to find a similar feature request and didn't find it. - [x] I checked the LangChain documentation and API reference to see if this feature already exists. - [x] This is not related to the langchain-community package. ### Package (Required) - [ ] langchain - [ ] langchain-openai - [ ] 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 - [x] langchain-openrouter - [ ] langchain-perplexity - [ ] langchain-qdrant - [ ] langchain-xai - [ ] Other / not sure / general ### Feature Description ## Feature request It would be great if `langchain-openrouter` supported the OpenRouter Responses API in the same way that `langchain-openai` supports OpenAI's Responses API via `use_responses_api=True`. ## Motivation OpenRouter now exposes both: - Chat Completions API - Responses API However, `ChatOpenRouter` currently only exposes the Chat Completions interface. Many production agent systems would benefit from the Responses API, especially for long-context and multi-turn agent workflows. ## Why this matters For production ReAct / LangGraph agents, the Responses API provides several important capabilities: - `previous_response_id` - Continue conversations without resending the entire conversation history. - Better conversation state management - Reduce prompt size for long-running agents. - Improved prompt caching - Especially useful for very large static system prompts (20k–100k+ tokens). - Future compatibility - OpenAI is investing new capabilities into the R…