Remove WebSocket wire format (#10179)

I'd like WireApi to go away (when chat is removed) and WebSockets is
still responses API just over a different transport.

codex-rs/core/src/models_manager/manager.rs

@@ -432,6 +432,7 @@ mod tests {
             stream_max_retries: Some(0),
             stream_idle_timeout_ms: Some(5_000),
             requires_openai_auth: false,
+            supports_websockets: false,
         }
     }