Add a GitHub workflow to close inactive issues and PRs automatically
diff --git a/.github/workflows/close-inactive-issues.yml b/.github/workflows/close-inactive-issues.yml
new file mode 100644
index 0000000000..d81b727aaa
--- /dev/null
+++ b/.github/workflows/close-inactive-issues.yml
@@ -0,0 +1,31 @@
+name: Close inactive issues
+
+on:
+  schedule:
+    - cron: "5 0 * * *"
+
+jobs:
+  close-issues:
+    runs-on: ubuntu-latest
+    permissions:
+      issues: write
+      pull-requests: write
+    steps:
+      - uses: actions/stale@v5
+        with:
+          days-before-issue-stale: 7
+          days-before-issue-close: 7
+          
+          days-before-pr-stale: 7
+          days-before-pr-close: 7
+          
+          stale-issue-label: "stale"
+          stale-pr-label: "stale"
+          
+          stale-issue-message: "Bumping this issue because it has been open for 7 days with no activity. Closing automatically in 7 days unless it becomes active again."
+          close-issue-message: "Closing due to inactivity."
+          
+          stale-pr-message: "Bumping this pull request because it has been open for 7 days with no activity. Closing automatically in 7 days unless it becomes active again."
+          close-pr-message: "Closing due to inactivity."
+          
+          repo-token: ${{ secrets.GITHUB_TOKEN }}

Way too many issues have been piling up with their authors disappearing and never closing them. At the same time, lots of the unmerged PRs remain completely unanswered due to their sheer irrelevance. Closing both would clean up a big portion of the clutter lingering on the project's page.