Fix Node version failure in publish workflow

Looks like the images got updated to v18 so they started failing.  For
npm install v16 and for Docker just run the script directly, it seems
silly to waste time installing v16 just to run a script through yarn.

.github/workflows/publish.yaml

@@ -29,6 +29,12 @@ jobs:
       - name: Checkout code-server
         uses: actions/checkout@v3
 
+      - name: Install Node.js v16
+        uses: actions/setup-node@v3
+        with:
+          node-version: "16"
+          cache: "yarn"
+
       - name: Download npm package from release artifacts
         uses: robinraju/release-downloader@v1.7
         with:
@@ -141,7 +147,7 @@ jobs:
           VERSION: ${{ env.VERSION }}
         run: |
           git checkout -b update-version-${{ env.VERSION }}
-          git add . 
+          git add .
           git commit -m "chore: updating version to ${{ env.VERSION }}"
           git push -u origin $(git branch --show)
           gh pr create --repo coder/code-server-aur --title "chore: bump version to ${{ env.VERSION }}" --body "PR opened by @$GITHUB_ACTOR" --assignee $GITHUB_ACTOR
@@ -186,7 +192,7 @@ jobs:
           out-file-path: "release-packages"
 
       - name: Publish to Docker
-        run: yarn publish:docker
+        run: ./ci/steps/docker-buildx-push.sh
         env:
           VERSION: ${{ env.VERSION }}
           GITHUB_TOKEN: ${{ github.token }}