When trying to use Fuxt in preview mode, it is including cookies in the request. The backend needs to be ready to accept these, otherwise a CORS error is thrown.
For example, see this error in Firefox when trying to fetch a draft page:

The problem is described here:
https://stackoverflow.com/a/69479005/503546
And the solution for WordPress WP JSON API is shown here:
https://stackoverflow.com/a/57951582/503546