Update release flow

Author: itspriddle

.github/workflows/release.yml

@@ -30,9 +30,18 @@ jobs:
         env:
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
 
+      - uses: actions/create-github-app-token@fee1f7d63c2ff003460e3d139729b119787bc349 # v2.2.2
+        id: app-token
+        with:
+          app-id: ${{ secrets.BUMP_APP_ID }}
+          private-key: ${{ secrets.BUMP_APP_PRIVATE_KEY }}
+          owner: built-fast
+          repositories: homebrew-devtools
+          permission-actions: write
+
       - name: Update Homebrew formula
         env:
-          GH_TOKEN: ${{ secrets.GH_TOKEN }}
+          GH_TOKEN: ${{ steps.app-token.outputs.token }}
         run: |
           gh workflow run bump-formula.yml \
             -f version="${GITHUB_REF_NAME}" \