How I can add more data to Laravel's auth()->user() object + it's relationships?

You can use global scope:

<?php

namespace App;

use Illuminate\Notifications\Notifiable;
use Illuminate\Database\Eloquent\Builder;
use Illuminate\Foundation\Auth\User as Authenticatable;

class User extends Authenticatable
{
    use Notifiable;

    /**
     * The attributes that are mass assignable.
     *
     * @var array
     */
    protected $fillable = [
        'name', 'email', 'password',
    ];

    /**
     * The attributes that should be hidden for arrays.
     *
     * @var array
     */
    protected $hidden = [
        'password', 'remember_token',
    ];

    public function person()
    {
        return $this->belongsTo(Person::class);
    }

    /**
     * The "booting" method of the model.
     *
     * @return void
     */
    protected static function boot()
    {
        parent::boot();

        static::addGlobalScope('withPerson', function (Builder $builder) {
            $builder->with(['person']);
        });
    }
}