fix(infra) - Fix merge queue skipper issues for chain e2e (#11810)

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

.github/workflows/test_chained_e2e.yml

@@ -29,6 +29,7 @@ permissions:
 jobs:
   merge_queue_skipper:
     name: 'Merge Queue Skipper'
+    permissions: 'read-all'
     runs-on: 'gemini-cli-ubuntu-16-core'
     outputs:
       skip: '${{ steps.merge-queue-e2e-skipper.outputs.skip-check }}'
@@ -37,6 +38,7 @@ jobs:
         uses: 'cariad-tech/merge-queue-ci-skipper@1032489e59437862c90a08a2c92809c903883772' # ratchet:cariad-tech/merge-queue-ci-skipper@main
         with:
           secret: '${{ secrets.GITHUB_TOKEN }}'
+    continue-on-error: true
 
   download_repo_name:
     runs-on: 'gemini-cli-ubuntu-16-core'
@@ -113,8 +115,12 @@ jobs:
 
   e2e_linux:
     name: 'E2E Test (Linux) - ${{ matrix.sandbox }}'
-    needs: 'parse_run_context'
+    needs:
+      - 'merge_queue_skipper'
+      - 'parse_run_context'
     runs-on: 'gemini-cli-ubuntu-16-core'
+    if: |
+      always() && (needs.merge_queue_skipper.result !='success' || needs.merge_queue_skipper.outputs.skip == 'false')
     strategy:
       fail-fast: false
       matrix:
@@ -161,8 +167,12 @@ jobs:
 
   e2e_mac:
     name: 'E2E Test (macOS)'
-    needs: 'parse_run_context'
+    needs:
+      - 'merge_queue_skipper'
+      - 'parse_run_context'
     runs-on: 'macos-latest'
+    if: |
+      always() && (needs.merge_queue_skipper.result !='success' || needs.merge_queue_skipper.outputs.skip == 'false')
     steps:
       - name: 'Checkout'
         uses: 'actions/checkout@08eba0b27e820071cde6df949e0beb9ba4906955' # ratchet:actions/checkout@v5
@@ -200,7 +210,7 @@ jobs:
       - 'merge_queue_skipper'
       - 'parse_run_context'
     if: |
-      needs.merge_queue_skipper.outputs.skip == 'false'
+      always() && (needs.merge_queue_skipper.result !='success' || needs.merge_queue_skipper.outputs.skip == 'false')
     runs-on: 'gemini-cli-windows-16-core'
     continue-on-error: true
 
@@ -258,7 +268,7 @@ jobs:
   e2e:
     name: 'E2E'
     if: |
-      always() && needs.merge_queue_skipper.outputs.skip == 'false'
+      always() && (needs.merge_queue_skipper.result !='success' || needs.merge_queue_skipper.outputs.skip == 'false')
     needs:
       - 'e2e_linux'
       - 'e2e_mac'