You are free to do with it as you like.
What I would do is create a relationship
User => HasMany => SocialProvider
SocialProvider will have a table with id, user_id, provider, provider_id for example
Then you can allow them to connect multiple accounts by simply adding additional SocialProviders.
You can still force them to create a password, but adding a nullable constraint to password field in users table and creating a middleware that redirects to a create password page if password is null.
Your socialite callback function would then look something like this.
public function callback($provider)
{
$callback = Socialite::driver('github')->stateless()->user();
$user = // Find User By Provider and Provider ID or create new user
Auth::login($user);
return redirect('/home');
}