custom session callback dosent return props.user

Environment

System:
OS: Linux 5.15 Ubuntu 22.04.1 LTS 22.04.1 LTS (Jammy Jellyfish)
CPU: (12) x64 Intel(R) Core(TM) i7-10750H CPU @ 2.60GHz
Memory: 24.44 GB / 31.26 GB
Container: Yes
Shell: 5.1.16 - /bin/bash
Binaries:
Node: 18.12.1 - ~/.nvm/versions/node/v18.12.1/bin/node
npm: 8.19.2 - ~/.nvm/versions/node/v18.12.1/bin/npm
Browsers:
Chrome: 107.0.5304.110
npmPackages:
next: ^13.0.3 => 13.0.5
next-auth: ^4.17.0 => 4.17.0
react: ^18.2.0 => 18.2.0

Reproduction URL

https://github.com/Swistek92/myApp

Describe the issue

https://next-auth.js.org/tutorials/role-based-login-strategy

said that:

/pages/api/auth/[...nextauth].js callbacks: { async session({ session, token, user }) { session.user.role = user.role; // Add role value to user object so it is passed along with session return session; } },

and in session props dosent include user object

https://stackoverflow.com/questions/73658567/nextauth-role-based-login-using-credentials/74650313#74650313

How to reproduce

create next13 app with custom role login system and when i wanna extends session object with role key, following https://next-auth.js.org/tutorials/role-based-login-strategy
there is not a user object into session props from with one i have to copy key

Expected behavior

callbacks: {
async session({session, token, user})
}
but
callbacks: {
async session({session, token})
}

Start with the linked myApp reproduction and compare its Next.js 13.0.5 and next-auth 4.17.0 configuration with the role-based login tutorial. Trace the session callback inputs and the resulting session props, using the reported credentials-based role flow. Done means the callback behavior is explained and the documented or observed discrepancy is resolved.