Not working with experience cloud with custom path

### Summary

Local DEV cannot load the site, if experience cloud is created with a custom path.

```
...my.site.com/xxx
```

It only works with experience cloud created at root without the custom path.

```
...my.site.com/
```

Here is the failure error messages when start the LWR website locally.
![Image](https://github.com/user-attachments/assets/fad90c5e-d617-4cc0-8c76-488e864b1c10)