Update the CI publish pipeline to be inline with PR checks (#7050)

# Pull Request

## 📖 Description

The publish pipeline needed updating to be inline with the PR pipeline.

## ✅ Checklist

### General

<!--- Review the list and put an x in the boxes that apply. -->

- [ ] I have included a change request file using `$ npm run change`
- [ ] I have added tests for my changes.
- [ ] I have tested my changes.
- [ ] I have updated the project documentation to reflect my changes.
- [x] I have read the [CONTRIBUTING](https://github.com/microsoft/fast/blob/master/CONTRIBUTING.md) documentation and followed the [standards](https://github.com/microsoft/fast/blob/master/CODE_OF_CONDUCT.md#our-standards) for this project.

.github/workflows/cd-release-npm.yml

@@ -16,7 +16,7 @@ jobs:
     strategy:
       matrix:
         node: [20.x]
-    if: contains('chrisdholt,janechu,nicholasrice,awentzel,eisenbergeffect', github.actor)
+    if: contains('chrisdholt,janechu', github.actor)
 
     steps:
     - uses: actions/checkout@v4
@@ -48,10 +48,20 @@ jobs:
       run: npm run checkchange
 
     - name: Testing Prettier format
-      run: npm run prettier:diff
+      run: npm run format:check
+
+    - name: Build workspaces
+      run: npm run build
+
+    - name: Install playwright dependencies and browsers
+      run: |
+        npx playwright install
 
     - name: Testing unit tests
-      run: npm run test --stream
+      run: npm run test
+
+    - name: Testing final validation
+      run: npm run test:validation
 
     - name: Publish NPM packages
       env: