Use otelbot app token for Tidy push (#1460)

Another attempt to get solution working for #1456.

It *almost* worked as expected in #1458 but I forgot an earlier lesson
from
[prepare-release](https://github.com/open-telemetry/otel-arrow/blob/382c61d4b35eaf8c4753b046d57aa7bc70d3b0e6/.github/workflows/prepare-release.yml#L133-L134)
that we have to inject the special otelbot app token as an environment
variable in the task that does the Git action. Otherwise, regular PR
workflows are not triggered.

I've seen some evidence that we should opt out of persisting regular git
creds from `checkout` in order for the `auth setup-git` to work. Would
like to try this configuration.

Author: drewrelmas

.github/workflows/tidy.yml

@@ -17,24 +17,31 @@ jobs:
         with:
           fetch-depth: 0
           ref: ${{ github.head_ref }}
+          persist-credentials: false
       - uses: actions/setup-go@44694675825211faa026b3c33043df3e48a5fa00 # v6.0.0
         with:
           go-version: "1.25.4"
       - name: make genotelarrowcol
         # This also runs 'go mod tidy' as part of its process
         run: make genotelarrowcol
       - name: Create GitHub App token
-        if: '!inputs.dry_run'
         uses: actions/create-github-app-token@67018539274d69449ef7c02e8e71183d1719ab42 # v2.1.4
         id: app-token
         with:
           app-id: ${{ vars.OTELBOT_APP_ID }}
           private-key: ${{ secrets.OTELBOT_PRIVATE_KEY }}
       - name: Commit changes
+        env:
+          # not using secrets.GITHUB_TOKEN since commits from that token do not trigger workflows
+          GH_TOKEN: ${{ steps.app-token.outputs.token }}
         run: |
           # Configure git for otelbot
           git config user.name otelbot
           git config user.email [email protected]
 
-          echo "git diff --exit-code || (git add . && git commit -m \"make genotelarrowcol\" && git push)"
-          git diff --exit-code || (git add . && git commit -m "make genotelarrowcol" && git push)
+          if ! git diff --exit-code; then
+            git add .
+            git commit -m "make genotelarrowcol"
+            gh auth setup-git
+            git push
+          fi