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/tests/chat_completions_payload.rs

@@ -60,6 +60,7 @@ async fn run_request(input: Vec<ResponseItem>) -> Value {
         stream_max_retries: Some(0),
         stream_idle_timeout_ms: Some(5_000),
         requires_openai_auth: false,
+        supports_websockets: false,
     };
 
     let codex_home = match TempDir::new() {