Standardize GitHub App Bot Authentication Across Workflows (#3582)

# Description of Changes

Please provide a summary of the changes, including:

- **What was changed**  
- Removed individual `actions/create-github-app-token` steps and
replaced them with a centralized `setup-bot` custom action across all
workflows.
- Updated steps to use `steps.setup-bot.outputs` instead of
`steps.generate-token.outputs`.
- Standardized step names and ordering (e.g. checkout before bot setup).
- Simplified `sync_files.yml` by eliminating the `read_bot_entries` job
and directly using `setup-bot` outputs.
- Added or adjusted permissions where required (e.g.
`repository-projects: write` in `licenses-update.yml`).

- **Why the change was made**  
- To centralize and standardize GitHub App authentication logic, reduce
duplication, and improve maintainability of CI workflows.
- To ensure a consistent bot identity (app slug, token,
committer/author) across all actions and PR automation.
- To streamline workflow configurations and make future updates easier.

---

## Checklist

### General

- [x] I have read the [Contribution
Guidelines](https://github.com/Stirling-Tools/Stirling-PDF/blob/main/CONTRIBUTING.md)
- [x] I have read the [Stirling-PDF Developer
Guide](https://github.com/Stirling-Tools/Stirling-PDF/blob/main/DeveloperGuide.md)
(if applicable)
- [ ] I have read the [How to add new languages to
Stirling-PDF](https://github.com/Stirling-Tools/Stirling-PDF/blob/main/HowToAddNewLanguage.md)
(if applicable)
- [x] I have performed a self-review of my own code
- [x] My changes generate no new warnings

### Documentation

- [ ] I have updated relevant docs on [Stirling-PDF's doc
repo](https://github.com/Stirling-Tools/Stirling-Tools.github.io/blob/main/docs/)
(if functionality has heavily changed)
- [ ] I have read the section [Add New Translation
Tags](https://github.com/Stirling-Tools/Stirling-PDF/blob/main/HowToAddNewLanguage.md#add-new-translation-tags)
(for new translation tags only)

### UI Changes (if applicable)

- [ ] Screenshots or videos demonstrating the UI changes are attached
(e.g., as comments or direct attachments in the PR)

### Testing (if applicable)

- [ ] I have tested my changes locally. Refer to the [Testing
Guide](https://github.com/Stirling-Tools/Stirling-PDF/blob/main/DeveloperGuide.md#6-testing)
for more details.

.github/workflows/check_properties.yml

@@ -15,7 +15,7 @@ jobs:
     runs-on: ubuntu-latest
     permissions:
       issues: write # Allow posting comments on issues/PRs
-      pull-requests: write
+      pull-requests: write # Allow writing to pull requests
     steps:
       - name: Harden Runner
         uses: step-security/harden-runner@0634a2670c59f64b4a01f0f96f84700a4088b9f0 # v2.12.0
@@ -25,10 +25,12 @@ jobs:
       - name: Checkout main branch first
         uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
 
-      - name: Set up Python
-        uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065 # v5.6.0
+      - name: Setup GitHub App Bot
+        id: setup-bot
+        uses: ./.github/actions/setup-bot
         with:
-          python-version: "3.12"
+          app-id: ${{ secrets.GH_APP_ID }}
+          private-key: ${{ secrets.GH_APP_PRIVATE_KEY }}
 
       - name: Get PR data
         id: get-pr-data
@@ -219,7 +221,7 @@ jobs:
             const comment = comments.data.find(c => c.body.includes("## 🚀 Translation Verification Summary"));
 
             // Only update or create comments by the action user
-            const expectedActor = "github-actions[bot]";
+            const expectedActor = "${{ steps.setup-bot.outputs.app-slug }}[bot]";
 
             if (comment && comment.user.login === expectedActor) {
               // Update existing comment