Fall back to http when websockets fail (#10139)

I expect not all proxies work with websockets, fall back to http if
websockets fail.

codex-rs/core/tests/responses_headers.rs

@@ -9,6 +9,7 @@ use codex_core::ModelProviderInfo;
 use codex_core::Prompt;
 use codex_core::ResponseEvent;
 use codex_core::ResponseItem;
+use codex_core::TransportManager;
 use codex_core::WEB_SEARCH_ELIGIBLE_HEADER;
 use codex_core::WireApi;
 use codex_core::models_manager::manager::ModelsManager;
@@ -94,6 +95,7 @@ async fn responses_stream_includes_subagent_header_on_review() {
         summary,
         conversation_id,
         session_source,
+        TransportManager::new(),
     )
     .new_session();
 
@@ -191,6 +193,7 @@ async fn responses_stream_includes_subagent_header_on_other() {
         summary,
         conversation_id,
         session_source,
+        TransportManager::new(),
     )
     .new_session();
 
@@ -346,6 +349,7 @@ async fn responses_respects_model_info_overrides_from_config() {
         summary,
         conversation_id,
         session_source,
+        TransportManager::new(),
     )
     .new_session();