Expose MCP server info as part of server status (#24698)

# Summary

Expose MCP server info via App Server (when available) so apps can
render a richer MCP experience

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

@@ -10964,6 +10964,47 @@
         "title": "McpResourceReadResponse",
         "type": "object"
       },
+      "McpServerInfo": {
+        "description": "Presentation metadata advertised by an initialized MCP server.",
+        "properties": {
+          "description": {
+            "type": [
+              "string",
+              "null"
+            ]
+          },
+          "icons": {
+            "items": true,
+            "type": [
+              "array",
+              "null"
+            ]
+          },
+          "name": {
+            "type": "string"
+          },
+          "title": {
+            "type": [
+              "string",
+              "null"
+            ]
+          },
+          "version": {
+            "type": "string"
+          },
+          "websiteUrl": {
+            "type": [
+              "string",
+              "null"
+            ]
+          }
+        },
+        "required": [
+          "name",
+          "version"
+        ],
+        "type": "object"
+      },
       "McpServerMigration": {
         "properties": {
           "name": {
@@ -11074,6 +11115,16 @@
             },
             "type": "array"
           },
+          "serverInfo": {
+            "anyOf": [
+              {
+                "$ref": "#/definitions/v2/McpServerInfo"
+              },
+              {
+                "type": "null"
+              }
+            ]
+          },
           "tools": {
             "additionalProperties": {
               "$ref": "#/definitions/v2/Tool"