[infra] Fix PR publisher comments (#177)

@mosuem I have no idea what I'm looking at, I copied this from dart-lang/tools#169.

Will this solve #175 ?

.github/workflows/post_summaries.yaml

@@ -0,0 +1,16 @@
+name: Comment on the pull request
+
+on:
+  # Trigger this workflow after the Health workflow completes. This workflow will have permissions to
+  # do things like create comments on the PR, even if the original workflow couldn't.
+  workflow_run:
+    workflows: 
+      - Publish
+    types:
+      - completed
+
+jobs:
+  upload:
+    uses: dart-lang/ecosystem/.github/workflows/post_summaries.yaml@main
+    permissions:
+      pull-requests: write

.github/workflows/publish.yaml

@@ -15,3 +15,5 @@ jobs:
     permissions:
       id-token: write # Required for authentication using OIDC
       pull-requests: write # Required for writing the pull request note
+    with:
+      write-comments: false

README.md

@@ -1,4 +1,3 @@
-[![dart](https://github.com/dart-lang/native/actions/workflows/dart.yaml/badge.svg)](https://github.com/dart-lang/native/actions/workflows/dart.yaml)
 [![Coverage Status](https://coveralls.io/repos/github/dart-lang/native/badge.svg?branch=main)](https://coveralls.io/github/dart-lang/native?branch=main)
 
 ## Overview