Update TypeSpec emitter version to prerelease 1.0.0-alpha.20251008.1 (#53093)

* Regenerate repository SDK with TypeSpec build 20251008.1

* Update SDK code ag_co_0

* revert unrelted dpg changes

---------

Co-authored-by: Wei Hu <[email protected]>

Author: azure-sdk

eng/azure-typespec-http-client-csharp-mgmt-emitter-package-lock.json

@@ -1,7 +1,7 @@
 {
   "main": "dist/src/index.js",
   "dependencies": {
-    "@azure-typespec/http-client-csharp-mgmt": "1.0.0-alpha.20250929.2"
+    "@azure-typespec/http-client-csharp-mgmt": "1.0.0-alpha.20251008.1"
   },
   "devDependencies": {
     "@azure-tools/typespec-azure-core": "0.60.0",