Fix action dependency (#6039)

### Description

Small bug in #6038, didn't remove the dependencies from other tasks.

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### Testing Instructions

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.github/workflows/nextjs-integration-test.yml

@@ -140,7 +140,7 @@ jobs:
   # Collect integration test results from execute_tests,
   # Store it as github artifact for next step to consume.
   collect_nextjs_integration_stat:
-    needs: [test-dev, test-prod, test-integration]
+    needs: [test-dev, test-integration]
     name: Next.js integration test status report
     runs-on: ubuntu-latest-8-core-oss
     if: always()
@@ -169,7 +169,7 @@ jobs:
             slack-payload.json
 
   upload_test_trace:
-    needs: [test-dev, test-prod, test-integration]
+    needs: [test-dev, test-integration]
     name: Upload test trace to datadog
     runs-on: ubuntu-latest-8-core-oss
     if: always()