Update private Playground instance to use dedicated CORS proxy (#56)

## Motivation for the change, related issues

The public CORS proxy does not support CORS for the private Playground
origin. We have configured a private CORS proxy to support that origin,
and we need to configure the private Playground instance to use that
proxy.

## Implementation details

This PR updates the private Playground deployment workflow to specify a
CORS proxy URL configured in the GitHub Actions environment.

## Testing Instructions (or ideally a Blueprint)

To save time , I am just going to deploy this update because this is a
simple change that I believe should work. I will test a deployment
immediately after merging to confirm.

Author: brandonpayton

.github/workflows/deploy-private-website.yml

@@ -33,7 +33,9 @@ jobs:
               with:
                   submodules: true
             - uses: ./.github/actions/prepare-playground
-            - run: npm run build
+            - env:
+                  CORS_PROXY_URL: ${{ vars.CORS_PROXY_URL }}
+            - run: npx nx build playground-website
 
             - name: Deploy to playground.wordpress.net
               shell: bash