In order to let Google Cloud CDN cache your CSS and JS files,
You'll need to modify the HTTP headers for CSS, JS files served from backend instance like the following:
Cache-control=Public
max-age
or s-maxage
directive, or an Expires
Since Google Cloud CDN does not provide console to configure the cache methods, the only way to do that is to modify the config files of your backend web server settings,
For example, httpd.conf or .htaccess for Apache HTTP Web Server, or nginx.conf for Nginx web server.
Map to your pre-built image, it'll be the Content Serving Nodes of the WordPress High Availability deployment, since only Content Serving Nodes are public-facing.
You can refer to the architecture diagram of WordPress High Availability:

Your host and URL paths are right, that's how WordPress High Availability works.
Only admin related URLs served by Admin Node, other requests will be served by Content Serving Nodes.
I would suggest you do the following:
- Ensure that you enabled the Cloud CDN on the Content Serving Nodes.
- SSH into the Admin Node, edit or create the
/var/www/html/.htaccess
file to modify the Cache Headers:
# Cache 1 Month for CSS and JS files
<filesMatch ".(css|js)$">
Header set Cache-Control "max-age=2592000, public"
</filesMatch>
- Wait for a few minutes to let the Content Serving Nodes get the update for Admin Node.
- Run the test again to see if it works.