[codex] include plan type in account updates (#13181)

This change fixes a Codex app account-state sync bug where clients could
know the user was signed in but still miss the ChatGPT subscription
tier, which could lead to incorrect upgrade messaging for paid users.

The root cause was that `account/updated` only carried `authMode` while
plan information was available separately via `account/read` and
rate-limit snapshots, so this update adds `planType` to
`account/updated`, populates it consistently across login and refresh
paths.

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

@@ -7319,6 +7319,16 @@
                 "type": "null"
               }
             ]
+          },
+          "planType": {
+            "anyOf": [
+              {
+                "$ref": "#/definitions/v2/PlanType"
+              },
+              {
+                "type": "null"
+              }
+            ]
           }
         },
         "title": "AccountUpdatedNotification",