Reuse realtime start for WebRTC

Move WebRTC SDP negotiation onto thread/realtime/start via an optional transport and emit the answer SDP as a realtime notification instead of returning it from a separate request.

Rebased onto latest origin/main and resolved conflicts by keeping the new endpoint re-export structure while adding realtime call support.

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

codex-rs/app-server-protocol/schema/json/ClientRequest.json

@@ -2857,6 +2857,48 @@
       ],
       "type": "object"
     },
+    "ThreadRealtimeStartTransport": {
+      "description": "EXPERIMENTAL - transport used by thread realtime.",
+      "oneOf": [
+        {
+          "properties": {
+            "type": {
+              "enum": [
+                "websocket"
+              ],
+              "title": "WebsocketThreadRealtimeStartTransportType",
+              "type": "string"
+            }
+          },
+          "required": [
+            "type"
+          ],
+          "title": "WebsocketThreadRealtimeStartTransport",
+          "type": "object"
+        },
+        {
+          "properties": {
+            "sdp": {
+              "description": "SDP offer generated by a WebRTC RTCPeerConnection after configuring audio and the realtime events data channel.",
+              "type": "string"
+            },
+            "type": {
+              "enum": [
+                "webrtc"
+              ],
+              "title": "WebrtcThreadRealtimeStartTransportType",
+              "type": "string"
+            }
+          },
+          "required": [
+            "sdp",
+            "type"
+          ],
+          "title": "WebrtcThreadRealtimeStartTransport",
+          "type": "object"
+        }
+      ]
+    },
     "ThreadResumeParams": {
       "description": "There are three ways to resume a thread: 1. By thread_id: load the thread from disk by thread_id and resume it. 2. By history: instantiate the thread from memory and resume it. 3. By path: load the thread from disk by path and resume it.\n\nThe precedence is: history > path > thread_id. If using history or path, the thread_id param will be ignored.\n\nPrefer using thread_id whenever possible.",
       "properties": {