Stabilize websocket response.failed error delivery (#14017)

## What changed
- Drop failed websocket connections immediately after a terminal stream
error instead of awaiting a graceful close handshake before forwarding
the error to the caller.
- Keep the success path and the closed-connection guard behavior
unchanged.

## Why this fixes the flake
- The failing integration test waits for the second websocket stream to
surface the model error before issuing a follow-up request.
- On slower runners, the old error path awaited
`ws_stream.close().await` before sending the error downstream. If that
close handshake stalled, the test kept waiting for an error that had
already happened server-side and nextest timed it out.
- Dropping the failed websocket immediately makes the terminal error
observable right away and marks the session closed so the next request
reconnects cleanly instead of depending on a best-effort close
handshake.

## Code or test?
- This is a production logic fix in `codex-api`. The existing websocket
integration test already exercises the regression path.

codex-rs/core/tests/suite/turn_state.rs

@@ -103,6 +103,7 @@ async fn websocket_turn_state_persists_within_turn_and_resets_after() -> Result<
             ]],
             response_headers: vec![(TURN_STATE_HEADER.to_string(), "ts-1".to_string())],
             accept_delay: None,
+            close_after_requests: true,
         },
         WebSocketConnectionConfig {
             requests: vec![vec![
@@ -112,6 +113,7 @@ async fn websocket_turn_state_persists_within_turn_and_resets_after() -> Result<
             ]],
             response_headers: Vec::new(),
             accept_delay: None,
+            close_after_requests: true,
         },
         WebSocketConnectionConfig {
             requests: vec![vec![
@@ -121,6 +123,7 @@ async fn websocket_turn_state_persists_within_turn_and_resets_after() -> Result<
             ]],
             response_headers: Vec::new(),
             accept_delay: None,
+            close_after_requests: true,
         },
     ])
     .await;