Refactor branch deletion for backports (opensearch-project#15983)

Signed-off-by: Sayali Gaikawad <gaiksaya@amazon.com>

.github/workflows/delete_backport_branch.yml

@@ -7,9 +7,16 @@ on:
 jobs:
   delete-branch:
     runs-on: ubuntu-latest
+    permissions:
+      contents: write
     if: startsWith(github.event.pull_request.head.ref,'backport/')
     steps:
       - name: Delete merged branch
-        uses: SvanBoxel/delete-merged-branch@main
-        env:
-          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+      uses: actions/github-script@v5
+      with:
+        script: |
+          github.rest.git.deleteRef({
+            owner: context.repo.owner,
+            repo: context.repo.repo,
+            ref: `heads/${context.payload.pull_request.head.ref}`,
+          })