Update GitHub Actions workflow for website publishing (#1129)

## Description
Alternate way of using GitHub secrets

### Why
Previous one us failing with 
<img width="823" height="133" alt="image"
src="https://github.com/user-attachments/assets/d376c65c-d3aa-4924-8d83-9e7f12e3ea1b"
/>


###### Microsoft Reviewers: [Open in
CodeFlow](https://microsoft.github.io/open-pr/?codeflow=https://github.com/microsoft/react-native-windows-samples/pull/1129)

Author: vineethkuttan

.github/workflows/website-publish.yml

@@ -1,3 +1,4 @@
+
 name: RNW Website Publish
 
 on:
@@ -13,21 +14,31 @@ jobs:
   publish_website:
     name: Website Publish
     runs-on: ubuntu-latest
+
     steps:
     - name: Git Setup
       run: |
         git config --global user.email "53619745+rnbot@users.noreply.github.com"
         git config --global user.name "React-Native-Windows Bot"
-        echo "machine github.com login 53619745+rnbot password ${{ secrets.RNBOT_GH_TOKEN }}" > ~/.netrc
-    - name: Git Checkout
-      uses: actions/checkout@v2
+        echo "machine github.com login x-access-token password ${RNBOT_GH_TOKEN}" > ~/.netrc
+      env:
+        RNBOT_GH_TOKEN: ${{ secrets.RNBOT_GH_TOKEN }}
+
+    - name: Checkout Repo
+      uses: actions/checkout@v4
+      with:
+        fetch-depth: 0  # required for gh-pages push
+
     - name: Yarn Install (Website)
       run: yarn install --frozen-lockfile
       working-directory: ./website
+
     - name: Publish to GitHub Pages
       env:
-        GIT_USER: 53619745+rnbot
+        GIT_USER: x-access-token
+        GIT_PASS: ${{ secrets.RNBOT_GH_TOKEN }}
       run: yarn run publish-gh-pages
       working-directory: ./website
-    - name: Git Cleanup
+
+    - name: Cleanup Netrc
       run: rm ~/.netrc