Replace Stale bot app with Action

Closes #1117.

.github/workflows/stale.yaml

@@ -0,0 +1,31 @@
+name: 'Mark stale issues and PRs'
+on:
+  schedule:
+    - cron: '7 8 * * *'
+
+permissions:
+  issues: write
+  pull-requests: write
+
+jobs:
+  stale:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/stale@v8
+        with:
+          # Number of days of inactivity before an issue becomes stale
+          days-before-stale: 60
+          # Number of days of inactivity before a stale issue is closed
+          days-before-close: -1
+          # Issues with these labels will never be considered stale
+          exempt-issue-labels: 'pinned,long-term,fixed in dev'
+          exempt-pr-labels: 'pinned,long-term,fixed in dev'
+          # Label to use when marking an issue as stale
+          stale-issue-label: stale
+          # Comment to post when marking an issue as stale. Set to `false` to disable
+          stale-issue-message: >
+            This issue has been automatically marked as stale because it has not had
+            recent activity.
+          stale-pr-message: >
+            This PR has been automatically marked as stale because it has not had
+            recent activity.