[Javascript Playground] AspireJavaScript.Angular installer fails because of another registry is referenced

### Is there an existing issue for this?

- [x] I have searched the existing issues

### Describe the bug

When trying to run the AspireWithJavascript playground, the angular app failed to start because the package-lock.json references this npm registry: `https://pkgs.dev.azure.com/dnceng/public/_packaging/dotnet-public-npm/npm/registry`

It's related to this PR #16855

### Expected Behavior

The Angular app doesn't reference a non public npm registry.

### Steps To Reproduce

1. Clone this
2. Go to `playground/AspireWithJavaScript`
3. Run `aspire run`
4. Go to the dashboard and see the angular-installer logs.

### Exceptions (if any)

```
983 verbose stack HttpErrorAuthUnknown: Unable to authenticate, need: Basic realm="https://pkgsprodcus2.pkgs.visualstudio.com/", Bearer, Bearer authorization_uri=https://login.windows.net/***, TFS-Federated
983 verbose stack at C:\Users\victo\AppData\Local\Volta\tools\image\node\24.11.1\node_modules\npm\node_modules\npm-registry-fetch\lib\check-response.js:88:17
983 verbose stack at process.processTicksAndRejections (node:internal/process/task_queues:103:5)
984 verbose statusCode 401
985 verbose pkgid ip-address@https://pkgs.dev.azure.com/dnceng/public/_packaging/dotnet-public-npm/npm/registry/ip-address/-/ip-address-10.2.0.tgz
986 error code E401
987 error Unable to authenticate, your authentication token seems to be invalid.
988 error To correct this please try logging in again with:
988 error npm login
```

### Aspire doctor output

_No response_

### Anything else?

_No response_

Start in playground/AspireWithJavaScript and inspect the Angular app's package-lock.json, then review related PR #16855 for context. Run aspire run and check the angular-installer logs; done means the Angular app no longer references the non-public Azure npm registry or requires authentication.

Written by the indexing model from the issue text.