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/ServerNotification.json

@@ -3304,6 +3304,22 @@
       ],
       "type": "object"
     },
+    "ThreadRealtimeSdpNotification": {
+      "description": "EXPERIMENTAL - emitted with the remote SDP for a WebRTC realtime session.",
+      "properties": {
+        "sdp": {
+          "type": "string"
+        },
+        "threadId": {
+          "type": "string"
+        }
+      },
+      "required": [
+        "sdp",
+        "threadId"
+      ],
+      "type": "object"
+    },
     "ThreadRealtimeStartedNotification": {
       "description": "EXPERIMENTAL - emitted when thread realtime startup is accepted.",
       "properties": {
@@ -4927,6 +4943,26 @@
       "title": "Thread/realtime/outputAudio/deltaNotification",
       "type": "object"
     },
+    {
+      "properties": {
+        "method": {
+          "enum": [
+            "thread/realtime/sdp"
+          ],
+          "title": "Thread/realtime/sdpNotificationMethod",
+          "type": "string"
+        },
+        "params": {
+          "$ref": "#/definitions/ThreadRealtimeSdpNotification"
+        }
+      },
+      "required": [
+        "method",
+        "params"
+      ],
+      "title": "Thread/realtime/sdpNotification",
+      "type": "object"
+    },
     {
       "properties": {
         "method": {