fix(infra) - Simplify cancel in progress and add permission to set status step (#11835)

Co-authored-by: gemini-cli-robot <gemini-cli-robot@google.com>

.github/workflows/test_chained_e2e.yml

@@ -18,9 +18,9 @@ on:
         required: true
 
 concurrency:
-  group: '${{ github.workflow }}-${{ github.head_ref || github.ref }}'
+  group: '${{ github.workflow }}-${{ github.head_ref || github.event.workflow_run.head_branch || github.ref }}'
   cancel-in-progress: |-
-    ${{ github.ref != 'refs/heads/main' && !startsWith(github.ref, 'refs/heads/release/') }}
+    ${{ github.event_name != 'push' && github.event_name != 'merge_group' }}
 
 permissions:
   contents: 'read'
@@ -99,6 +99,7 @@ jobs:
 
   set_pending_status:
     runs-on: 'gemini-cli-ubuntu-16-core'
+    permissions: 'write-all'
     if: "github.event_name == 'workflow_dispatch' || github.event_name == 'workflow_run'"
     needs:
       - 'parse_run_context'
@@ -286,6 +287,7 @@ jobs:
 
   set_workflow_status:
     runs-on: 'gemini-cli-ubuntu-16-core'
+    permissions: 'write-all'
     if: "github.event_name == 'workflow_dispatch' || github.event_name == 'workflow_run'"
     needs:
       - 'parse_run_context'

.github/workflows/trigger_e2e.yml

@@ -15,7 +15,7 @@ jobs:
     steps:
       - name: 'Save Repo name'
         env:
-          # Replace with github.event.pull_request.base.repo.full_name when switched to listen on pull request events. This repo name does not contain the org which is needed for checkout.
+          # Replace with github.event.pull_request.head.repo.full_name when switched to listen on pull request events. This repo name does not contain the org which is needed for checkout.
           REPO_NAME: '${{ github.event.repository.name }}'
         run: |
           mkdir -p ./pr