`ProviderToolSearchMiddleware` defers tools as flat top-level functions instead of wrapping them in a `namespace` — no token savings

### Submission checklist - [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) - [x] langchain - [x] 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 - [ ] langchain-openrouter - [ ] langchain-perplexity - [ ] langchain-qdrant - [ ] langchain-xai - [ ] Other / not sure / general ### Related Issues / PRs _No response_ ### Reproduction Steps / Example Code (Python) ```python Three identical requests to the OpenAI Responses API (`gpt-5.4-mini`), differing only in how the tools are encoded: | # | tools encoding | `usage.input` | vs inline | |---|---|--:|--:| | A | inline `function` (no defer) | 1992 | — | | B | **flat** `function` + `defer_loading:true` + `tool_search` *(what the middleware sends)* | **2469** | **+24%** | | C | `tool_search` + `namespace` wrapping the deferred `function`s | **1063** | **−47%** | Form **C** is what produces the intended savings; **B** (the middleware's form) regresses. Minimal repro of the payload difference: specs = [...] # 14 {"name","description","parameters"} tool dicts # B — what ProviderToolSearchMiddleware emits today tools_flat = [{"type": "function", **s, "defer_loading": True} for s…