Chore: Add stale issue/PR checker (#15151)

Author: nzakas

.github/workflows/stale.yml

@@ -0,0 +1,28 @@
+# This workflow warns and then closes issues and PRs that have had no activity for a specified amount of time.
+#
+# You can adjust the behavior by modifying this file.
+# For more information, see:
+# https://github.com/actions/stale
+name: Mark stale issues and pull requests
+
+on:
+  schedule:
+  - cron: '31 22 * * *'
+
+jobs:
+  stale:
+
+    runs-on: ubuntu-latest
+    permissions:
+      issues: write
+      pull-requests: write
+
+    steps:
+    - uses: actions/stale@v3
+      with:
+        repo-token: ${{ secrets.GITHUB_TOKEN }}
+        days-before-stale: 60
+        days-before-close: 7
+        stale-issue-message: 'Oops! It looks like we lost track of this issue. @eslint/eslint-tsc what do we want to do here? This issue will auto-close in 7 days without an update.'
+        stale-pr-message: 'Oops! It looks like we lost track of this pull request. @eslint/eslint-tsc what do we want to do here? This pull request will auto-close in 7 days without an update.'
+        exempt-all-assignees: true