Send model calls to a Responses endpoint

Send model calls to a Responses endpoint

One client sends every model call of an agent. The ChatGPT backend and
the OpenAI API take the same request body, so the client differs between
them only in its URL and its credentials. Each request sets store to
false and stream to true, sends the input as a list, asks for the
encrypted reasoning, and carries the fixed cache key of the agent, so
the turns and the compactions share one prompt cache. It never sends
max_output_tokens or metadata, which the ChatGPT backend refuses.

The client reads the event stream until the response completes and fails
on a failed, incomplete, or cut stream. Each call, also a failed one,
adds a line to usage.jsonl with the model, the input, cached, and output
tokens, the HTTP status, and the x-codex-* quota headers.

Issue: b14d537