When you login with a user you will get a token back. You can then use the token and make a call to /users/me and it will give the role back in that response. It’s an extra call but saves you from modifying the auth local login provider etc.
In the response you can do response.role.name to get the name of the role it’s an object looking like this
Since Strapi version 4.2.2 the route api/users/me no longer returns the role field in the user data but accepts populating (see https://github.com/strapi/strapi/issues/13296).
So now to get the user’s role you need to populate the role field, thus the call will be api/users/me?populate=role.
Note that you also need to give the role permissions to find role too.