Deflake realtime handoff steering test (#28300)

## Summary
- keep the realtime mock websocket open for the handoff steering test
after scripted responses
- avoid racing the mock server close before the standalone handoff
append is observed, which was showing up as a Windows timeout in CI

__Details__:
Failures in samples seem to be caused by:
1. The mock websocket sends conversation.handoff.requested.
2. The mock immediately closes the websocket because
start_websocket_server(...) defaults to close_after_requests: true.
3. On Windows, that close often surfaces as os error 10053 / 10054.
4. The realtime stream shuts down before the routed handoff finishes
creating/steering the follow-up request.
5. The test waits for the expected follow-up event and times out.

The PR changes only step 2: for this test, the mock websocket stays open
after sending the scripted handoff event. The same handoff event is
still sent, and the test still asserts the important steering behavior:
1. first Responses request has the original prompt
2. first request does not contain realtime delegation
3. second Responses request does contain the realtime delegation

## Validation
- `just fmt`
- `just test -p codex-core --test all
suite::realtime_conversation::inbound_handoff_request_steers_active_turn`

## Recent CI failures with the same signature

-
https://github.com/openai/codex/actions/runs/27538033492/job/81392362858
  - 2026-06-15, `[codex] update multi-agent v2 prompts`
- same test failed after `conversation.handoff.requested`; websocket
read failed with `os error 10053`

-
https://github.com/openai/codex/actions/runs/27543877820/job/81412200651
- 2026-06-15, `feat: dispatch queued user messages through core idle
extensions`
  - same test failed; websocket read failed with `os error 10054`

-
https://github.com/openai/codex/actions/runs/27544342375/job/81413801641
  - 2026-06-15, `[codex] Make marketplace loading capability aware`
  - same test failed; websocket read failed with `os error 10053`

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

@@ -3579,24 +3579,29 @@ async fn inbound_handoff_request_steers_active_turn() -> Result<()> {
     let (api_server, completions) =
         start_streaming_sse_server(vec![first_chunks, second_chunks]).await;
 
-    let realtime_server = start_websocket_server(vec![vec![
-        vec![json!({
-            "type": "session.updated",
-            "session": { "id": "sess_steer", "instructions": "backend prompt" }
-        })],
-        vec![
-            json!({
-                "type": "conversation.input_transcript.delta",
-                "delta": "steer via realtime"
-            }),
-            json!({
-                "type": "conversation.handoff.requested",
-                "handoff_id": "handoff_steer",
-                "item_id": "item_steer",
-                "input_transcript": "steer via realtime"
-            }),
+    let realtime_server = start_websocket_server_with_headers(vec![WebSocketConnectionConfig {
+        requests: vec![
+            vec![json!({
+                "type": "session.updated",
+                "session": { "id": "sess_steer", "instructions": "backend prompt" }
+            })],
+            vec![
+                json!({
+                    "type": "conversation.input_transcript.delta",
+                    "delta": "steer via realtime"
+                }),
+                json!({
+                    "type": "conversation.handoff.requested",
+                    "handoff_id": "handoff_steer",
+                    "item_id": "item_steer",
+                    "input_transcript": "steer via realtime"
+                }),
+            ],
         ],
-    ]])
+        response_headers: Vec::new(),
+        accept_delay: None,
+        close_after_requests: false,
+    }])
     .await;
 
     let mut builder = test_codex().with_model("gpt-5.4").with_config({