[codex] Support sequential cutoff reasoning summaries (#31306)

## Summary

When enabled for the OpenAI provider, Codex sends
`stream_options.reasoning_summary_delivery = "sequential_cutoff"` on
HTTP and
WebSocket requests, including prewarm, and renders completed summary
sections
from `reasoning_summary_text.done`. Flag-off and non-OpenAI behavior is
unchanged.

## Expected rollout

```text
reasoning 0 added
summary 0 done
summary 1 done
summary 2 starts
summary 2 cancelled / incomplete
reasoning 0 done  <-- cancel summary 2 work and mark it incomplete
message 1 added
message 1 text streams
message 1 completed
```

Depends on
[openai/openai#1096660](https://github.com/openai/openai/pull/1096660).

codex-rs/codex-api/tests/clients.rs

@@ -321,6 +321,7 @@ async fn responses_client_stream_request_preserves_item_ids() -> Result<()> {
         reasoning: None,
         store: false,
         stream: true,
+        stream_options: None,
         include: Vec::new(),
         service_tier: None,
         prompt_cache_key: None,
@@ -407,6 +408,7 @@ async fn streaming_client_retries_on_transport_error() -> Result<()> {
         reasoning: None,
         store: false,
         stream: true,
+        stream_options: None,
         include: Vec::new(),
         service_tier: None,
         prompt_cache_key: None,
@@ -526,6 +528,7 @@ async fn azure_store_sends_ids_and_headers() -> Result<()> {
         reasoning: None,
         store: true,
         stream: true,
+        stream_options: None,
         include: Vec::new(),
         service_tier: None,
         prompt_cache_key: None,