feat(codex): implement /btw /async slash command path

codex-rs/app-server-protocol/schema/json/codex_app_server_protocol.schemas.json

@@ -482,6 +482,30 @@
           "title": "Thread/shellCommandRequest",
           "type": "object"
         },
+        {
+          "properties": {
+            "id": {
+              "$ref": "#/definitions/v2/RequestId"
+            },
+            "method": {
+              "enum": [
+                "thread/asyncTask/start"
+              ],
+              "title": "Thread/asyncTask/startRequestMethod",
+              "type": "string"
+            },
+            "params": {
+              "$ref": "#/definitions/v2/ThreadAsyncTaskStartParams"
+            }
+          },
+          "required": [
+            "id",
+            "method",
+            "params"
+          ],
+          "title": "Thread/asyncTask/startRequest",
+          "type": "object"
+        },
         {
           "properties": {
             "id": {
@@ -12448,6 +12472,35 @@
         "title": "ThreadArchivedNotification",
         "type": "object"
       },
+      "ThreadAsyncTaskStartParams": {
+        "$schema": "http://json-schema.org/draft-07/schema#",
+        "properties": {
+          "input": {
+            "items": {
+              "$ref": "#/definitions/v2/UserInput"
+            },
+            "type": "array"
+          },
+          "taskId": {
+            "type": "string"
+          },
+          "threadId": {
+            "type": "string"
+          }
+        },
+        "required": [
+          "input",
+          "taskId",
+          "threadId"
+        ],
+        "title": "ThreadAsyncTaskStartParams",
+        "type": "object"
+      },
+      "ThreadAsyncTaskStartResponse": {
+        "$schema": "http://json-schema.org/draft-07/schema#",
+        "title": "ThreadAsyncTaskStartResponse",
+        "type": "object"
+      },
       "ThreadClosedNotification": {
         "$schema": "http://json-schema.org/draft-07/schema#",
         "properties": {