Add WebRTC transport to realtime start (#16960)

Adds WebRTC startup to the experimental app-server
`thread/realtime/start` method with an optional transport enum. The
websocket path remains the default; WebRTC offers create the realtime
session through the shared start flow and emit the answer SDP via
`thread/realtime/sdp`.

---------

Co-authored-by: Codex <noreply@openai.com>

codex-rs/core/src/client.rs

@@ -39,6 +39,8 @@ use codex_api::MemoriesClient as ApiMemoriesClient;
 use codex_api::MemorySummarizeInput as ApiMemorySummarizeInput;
 use codex_api::MemorySummarizeOutput as ApiMemorySummarizeOutput;
 use codex_api::RawMemory as ApiRawMemory;
+use codex_api::RealtimeCallClient as ApiRealtimeCallClient;
+use codex_api::RealtimeSessionConfig;
 use codex_api::Reasoning;
 use codex_api::RequestTelemetry;
 use codex_api::ReqwestTransport;
@@ -443,6 +445,30 @@ impl ModelClient {
             .map_err(map_api_error)
     }
 
+    pub async fn create_realtime_call(
+        &self,
+        sdp: String,
+        session_config: RealtimeSessionConfig,
+    ) -> Result<String> {
+        self.create_realtime_call_with_headers(sdp, session_config, ApiHeaderMap::new())
+            .await
+    }
+
+    pub async fn create_realtime_call_with_headers(
+        &self,
+        sdp: String,
+        session_config: RealtimeSessionConfig,
+        extra_headers: ApiHeaderMap,
+    ) -> Result<String> {
+        let client_setup = self.current_client_setup().await?;
+        let transport = ReqwestTransport::new(build_reqwest_client());
+        ApiRealtimeCallClient::new(transport, client_setup.api_provider, client_setup.api_auth)
+            .create_with_session_and_headers(sdp, session_config, extra_headers)
+            .await
+            .map(|response| response.sdp)
+            .map_err(map_api_error)
+    }
+
     /// Builds memory summaries for each provided normalized raw memory.
     ///
     /// This is a unary call (no streaming) to `/v1/memories/trace_summarize`.