Add action to close PRs with merge conflicts (#9561)

.github/workflows/repo-stale.yaml

@@ -1,4 +1,4 @@
-name: Issue Stale Check
+name: Stale Check
 
 on:
   schedule:
@@ -7,8 +7,11 @@ on:
 
 permissions:
   issues: write
+  pull-requests: write
+
 jobs:
-  stale:
+  issues:
+    name: Check issues
     runs-on: ubuntu-latest
     if: ${{ contains(github.repository, 'jellyfin/') }}
     steps:
@@ -28,3 +31,21 @@ jobs:
             If you're the original submitter of this issue, please comment confirming if this issue still affects you in the latest release or master branch, or close the issue if it has been fixed. If you're another user also affected by this bug, please comment confirming so. Either action will remove the stale label.
 
             This bot exists to prevent issues from becoming stale and forgotten. Jellyfin is always moving forward, and bugs are often fixed as side effects of other changes. We therefore ask that bug report authors remain vigilant about their issues to ensure they are closed if fixed, or re-confirmed - perhaps with fresh logs or reproduction examples - regularly. If you have any questions you can reach us on [Matrix or Social Media](https://docs.jellyfin.org/general/getting-help.html).
+
+  prs-conflicts:
+    name: Check PRs with merge conflicts
+    runs-on: ubuntu-latest
+    if: ${{ contains(github.repository, 'jellyfin/') }}
+    steps:
+      - uses: actions/stale@6f05e4244c9a0b2ed3401882b05d701dd0a7289b # v7.0.0
+        with:
+          repo-token: ${{ secrets.JF_BOT_TOKEN }}
+          operations-per-run: 75
+          # The merge conflict action will remove the label when updated
+          remove-stale-when-updated: false
+          days-before-stale: -1
+          days-before-close: 90
+          days-before-issue-close: -1
+          stale-pr-label: merge conflict
+          close-pr-message: |-
+            This PR has been closed due to having unresolved merge conflicts.