feat(exa): add integration header and update search types

### 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 - [x] langchain-exa - [ ] langchain-fireworks - [ ] langchain-groq - [ ] langchain-huggingface - [ ] langchain-mistralai - [ ] langchain-nomic - [ ] langchain-ollama - [ ] langchain-openrouter - [ ] langchain-perplexity - [ ] langchain-qdrant - [ ] langchain-xai - [ ] Other / not sure / general ### Feature Description Two small additive changes to the langchain-exa partner package: 1. Integration header, adds x-exa-integration: langchain-integration header to all Exa API requests for usage analytics. No effect on request/response behavior. 2. Search type update, the type Literal currently includes neural and keyword which are deprecated. Updated to auto, deep, fast to match the current API. No function signatures changed, no defaults changed, no breaking changes. Both changes are additive only. ### Use Case Updating the exa integration to the latest API spec. ### Proposed Solution _No response_ ### Alternatives Considered _No response_ ### Additional Context _No response_