ci: track meaningful pull request inactivity

Use human activity and observed head changes because GitHub can update PR timestamps without contributor activity.

Audit every open PR before applying changes and start existing PRs from a safe baseline.

.github/workflows/stale-prs.yml

@@ -0,0 +1,41 @@
+name: Stale Pull Requests
+
+on:
+  schedule:
+    - cron: "30 3 * * *"
+  workflow_dispatch:
+    inputs:
+      mode:
+        description: Run without changes or apply the PR inactivity policy
+        type: choice
+        required: true
+        default: dry-run
+        options:
+          - dry-run
+          - apply
+
+permissions:
+  contents: read
+  issues: write
+  pull-requests: write
+
+concurrency:
+  group: stale-pull-requests
+  cancel-in-progress: false
+
+jobs:
+  stale-prs:
+    name: Check Every Open PR
+    runs-on: ubuntu-latest
+    timeout-minutes: 15
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7.0.1
+      - uses: actions/setup-node@820762786026740c76f36085b0efc47a31fe5020 # v7.0.0
+        with:
+          node-version: 24
+      - name: Check PR inactivity
+        env:
+          GITHUB_TOKEN: ${{ github.token }}
+          GITHUB_REPOSITORY: ${{ github.repository }}
+          RUN_MODE: ${{ github.event_name == 'schedule' && 'apply' || inputs.mode }}
+        run: node scripts/stale-prs/run.mjs "--${RUN_MODE}"