Try to use the built in token instead of a PAT

.github/workflows/sync-main-doc.yml

@@ -8,11 +8,11 @@ jobs:
   sync:
     runs-on: ubuntu-latest
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
         with:
           ref: main
 
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
         with:
           repository: quarkusio/quarkus
           path: .quarkus-main-repository
@@ -58,13 +58,7 @@ jobs:
             git commit -am "Sync documentation of main branch"
           fi
           git pull origin main --rebase
-      - name: Push changes to main branch
-        # Uses sha for added security since tags can be updated
-        uses: ad-m/github-push-action@057a6ba835d986bfe495dd476a6c4db1d5f9503c
-        with:
-          github_token: ${{ secrets.SYNC_MAIN_TOKEN }}
-          branch: main
-
+          git push origin main
       - name: Report status
         if: "always() && github.repository == 'quarkusio/quarkusio.github.io'"
         shell: bash