CP: Use packages/packages recipe. (#122822) (#122842)

* Use packages/packages recipe. (#122822)

Use packages/packages recipe.

* Fix conflicts.

* Do not add tests that didn't exist.

* Remove name change caused by conflict resolution.
diff --git a/.ci.yaml b/.ci.yaml
index 2c801ce..b6cde49 100644
--- a/.ci.yaml
+++ b/.ci.yaml
@@ -4655,7 +4655,7 @@
       task_name: flutter_tool_startup__macos
 
   - name: Linux flutter_packaging
-    recipe: packaging_v2/packaging_v2
+    recipe: packaging/packaging
     timeout: 60
     scheduler: release
     bringup: true
@@ -4669,7 +4669,7 @@
         ["framework", "hostonly", "shard", "linux"]
 
   - name: Mac flutter_packaging
-    recipe: packaging_v2/packaging_v2
+    recipe: packaging/packaging
     timeout: 60
     scheduler: release
     bringup: true
@@ -4685,7 +4685,7 @@
       cpu: "x86"
 
   - name: Mac_arm64 flutter_packaging
-    recipe: packaging_v2/packaging_v2
+    recipe: packaging/packaging
     timeout: 60
     scheduler: release
     bringup: true
@@ -4701,7 +4701,7 @@
       cpu: "arm64"
 
   - name: Windows flutter_packaging
-    recipe: packaging_v2/packaging_v2
+    recipe: packaging/packaging
     timeout: 60
     scheduler: release
     bringup: true