ChatGPT's Codex endpoint now rejects requests whose input replays a hosted
web_search_call item unless tools declares web_search, failing the stream
with "response protection is unavailable". Codex local context compaction
sends the full history with tools:[], so every compaction after a web search
fails and the session gets stuck in a reconnect loop.
For OAuth transform, passthrough and WebSocket paths, append a cached-only
web_search tool when the history contains web_search_call and no web_search
tool is declared. When the caller offered no tools, pin tool_choice to
"none" so the injected tool cannot be invoked. The /responses/compact wire
shape is left untouched.
Fixes#7927
