For this purpose, if a user is passwordless or has a password set up, you can use the API endpoint /publisher/users/get (with the parameters as described here).
The response parameter password can have the following values:
has-password
expired-non-usable
passwordless-non-usable
A sample Sandbox curl request can be found below:
curl --location --request POST 'https://sandbox.piano.io/id/api/v1/publisher/users/get?api_token=<api_token>&uid=<uid>&aid=<aid>' \
The password status of a user can currently be retrieved also on the front-end as described here.