ci: Automatically clear caches for closed PRs (getsentry#13354)

Taken from
https://github.com/actions/cache/blob/main/tips-and-workarounds.md#force-deletion-of-caches-overriding-default-cache-eviction-policy.

Caches are per-branch, so if a PR is closed we do not need to keep any
caches for that branch around anymore. This PR adds automation to do
just that.

.github/workflows/cleanup-pr-caches.yml

@@ -0,0 +1,38 @@
+name: "Automation: Cleanup PR caches"
+on:
+  pull_request:
+    types:
+      - closed
+
+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: Check out code
+        uses: actions/checkout@v4
+
+      - name: Cleanup
+        run: |
+          gh extension install actions/gh-actions-cache
+
+          REPO=${{ github.repository }}
+          BRANCH=refs/pull/${{ github.event.pull_request.number }}/merge
+
+          echo "Fetching list of cache key"
+          cacheKeysForPR=$(gh actions-cache list -R $REPO -B $BRANCH | cut -f 1 )
+
+          ## Setting this to not fail the workflow while deleting cache keys.
+          set +e
+          echo "Deleting caches..."
+          for cacheKey in $cacheKeysForPR
+          do
+              gh actions-cache delete $cacheKey -R $REPO -B $BRANCH --confirm
+          done
+          echo "Done"
+        env:
+          GH_TOKEN: ${{ secrets.GITHUB_TOKEN }}