Update publish.yaml (#2269)

Do not write comments in `publish.yaml`, as they are written in
`post_summaries.yaml`. This makes comments possible on forks.

- Thanks for your contribution! Please replace this text with a
description of what this PR is changing or adding and why, list any
relevant issues, and review the contribution guidelines below.

---

- [x] I’ve reviewed the contributor guide and applied the relevant
portions to this PR.

<details>
  <summary>Contribution guidelines:</summary><br>

- See our [contributor
guide](https://github.com/dart-lang/.github/blob/main/CONTRIBUTING.md)
for general expectations for PRs.
- Larger or significant changes should be discussed in an issue before
creating a PR.
- Contributions to our repos should follow the [Dart style
guide](https://dart.dev/guides/language/effective-dart) and use `dart
format`.
- Most changes should add an entry to the changelog and may need to [rev
the pubspec package
version](https://github.com/dart-lang/sdk/blob/main/docs/External-Package-Maintenance.md#making-a-change).
- Changes to packages require [corresponding
tests](https://github.com/dart-lang/.github/blob/main/CONTRIBUTING.md#Testing).

Note that many Dart repos have a weekly cadence for reviewing PRs -
please allow for some latency before initial review feedback.
</details>

Author: mosuem

.github/workflows/publish.yaml

@@ -13,3 +13,5 @@ jobs:
   publish:
     if: ${{ github.repository_owner == 'dart-lang' }}
     uses: dart-lang/ecosystem/.github/workflows/publish.yaml@main
+    with:
+      write-comments: false