revert: 'chore(IDX): replace PAT with GH App' (#2886)

For some reason this isn't working as expected, so I need to revert
before I can look into this more.

Reverts #2863

.github/workflows/sync-public-with-private.yml

@@ -13,25 +13,17 @@ jobs:
       image: ghcr.io/dfinity/minimal-runner-image:0.1
     if: ${{ github.repository != 'dfinity/ic' }}
     steps:
-      - name: Create GitHub App Token
-        uses: actions/create-github-app-token@v1
-        id: app-token
-        with:
-          # The app used for this is actually PR_AUTOMATION_BOT_PRIVATE, but because the env
-          # vars need to be the same across both repos, we use the same names as the public one
-          app-id: ${{ vars.PR_AUTOMATION_BOT_PUBLIC_APP_ID }}
-          private-key: ${{ secrets.PR_AUTOMATION_BOT_PUBLIC_PRIVATE_KEY }}
-      - name: Checkout
-        uses: actions/checkout@v4
-        with:
-          ref: 'master-private'
-          token: ${{ steps.app-token.outputs.token }}
-
-      - name: Sync changes from public ic
-        run: |
-          git config --global user.name "IDX GitHub Automation"
-          git config --global user.email "idx@dfinity.org"
-  
-          git remote add public https://github.com/dfinity/ic.git
-          git fetch public master
-          git push origin public/master:master-private
+    - name: Checkout
+      uses: actions/checkout@v4
+      with:
+        ref: 'master-private'
+        token: ${{ secrets.PUSH_TO_IC_PRIVATE }}
+
+    - name: Sync changes from public ic
+      run: |
+        git config --global user.name "IDX GitHub Automation"
+        git config --global user.email "idx@dfinity.org"
+
+        git remote add public https://github.com/dfinity/ic.git
+        git fetch public master
+        git push origin public/master:master-private