[ci] Add daily stale branch cache cleanup (#32691)

Cleans up stale non-main caches daily
---
[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/facebook/react/pull/32691).
* #32692
* __->__ #32691

.github/workflows/shared_cleanup_stale_branch_caches.yml

@@ -0,0 +1,33 @@
+# https://github.com/actions/cache/blob/main/tips-and-workarounds.md#force-deletion-of-caches-overriding-default-cache-eviction-policy
+
+name: (Shared) Cleanup Stale Branch Caches
+on:
+  schedule:
+    - cron: 0 0 * * *
+  workflow_dispatch:
+
+jobs:
+  cleanup:
+    runs-on: ubuntu-latest
+    permissions:
+      # `actions:write` permission is required to delete caches
+      #   See also: https://docs.github.com/en/rest/actions/cache?apiVersion=2022-11-28#delete-a-github-actions-cache-for-a-repository-using-a-cache-id
+      actions: write
+      contents: read
+    steps:
+      - name: Cleanup
+        run: |
+          echo "Fetching list of cache keys"
+          cacheKeysForPR=$(gh cache list --limit 100 --json id,ref --jq '.[] | select(.ref != "refs/heads/main") | .id')
+
+          ## Setting this to not fail the workflow while deleting cache keys.
+          set +e
+          for cacheKey in $cacheKeysForPR
+          do
+              gh cache delete $cacheKey
+              echo "Deleting $cacheKey"
+          done
+          echo "Done"
+        env:
+          GH_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+          GH_REPO: ${{ github.repository }}