Responses API over WebSocket

Upgrades the connection to a WebSocket and runs the OpenAI Responses API
in WebSocket Mode. Clients send response.create events on the socket and
receive streamed events through the standard inference pipeline (PreLLMHook,
key selection, provider call, PostLLMHook).

Auth is identical to the HTTP POST variant — Bearer/Basic/Virtual Key/API Key
may be supplied as request headers on the upgrade request. The OpenAI SDK can
also pass an API key via the openai-insecure-api-key.<key> WebSocket
subprotocol.

This GET endpoint shares its path with the POST inference endpoint; route
selection is based on the Upgrade: websocket request header.