chore(testing): set branch name

.github/workflows/integration-testing.yaml

@@ -1,12 +1,13 @@
 name: Run Integration Tests
 on:
-  merge_group: {}
+  push:
+    branches:
+      - playwright_integration
 
 concurrency: integration_environment
 
 jobs:
   variables:
-    if: github.event.check_run.pull_requests[0].base.ref == 'playwright_integration'
     runs-on: ubuntu-latest
     outputs:
       date: ${{ steps.data.outputs.date }}