docs: Add repository mirroring guide and GitHub Actions

- Complete mirroring guide (GitHub ↔ Gitea)
- GitHub Actions workflow to sync to Gitea
- Mirror status check workflow
- SSH and token authentication methods
- Troubleshooting guide

.github/workflows/mirror-check.yml

@@ -0,0 +1,35 @@
+name: Mirror Status Check
+
+on:
+  schedule:
+    - cron: '0 */6 * * *'  # Every 6 hours
+  workflow_dispatch:
+
+jobs:
+  check-sync:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Check if repositories are in sync
+        run: |
+          # Get latest commit from GitHub
+          GITHUB_SHA=$(curl -s \
+            -H "Authorization: token ${{ secrets.GITHUB_TOKEN }}" \
+            "https://api.github.com/repos/terraphim/gitea-infrastructure/commits/main" | \
+            jq -r '.sha')
+          
+          # Get latest commit from Gitea
+          GITEA_SHA=$(curl -s \
+            -H "Authorization: token ${{ secrets.GITEA_TOKEN }}" \
+            "https://git.terraphim.cloud/api/v1/repos/terraphim/gitea-infrastructure/commits/main" | \
+            jq -r '.sha')
+          
+          echo "GitHub: ${GITHUB_SHA:0:7}"
+          echo "Gitea:  ${GITEA_SHA:0:7}"
+          
+          if [ "$GITHUB_SHA" == "$GITEA_SHA" ]; then
+            echo "✅ Repositories are in sync"
+            exit 0
+          else
+            echo "⚠️ Repositories are OUT OF SYNC"
+            exit 1
+          fi