Recovers old values and data stored in database checkbox multi array

hello, (again) before i begin srry for my bad english.

it's school project : An user can post a demande, with a form :

the form recovers info of the demande(title, body...) and infos of the student(name, regions, skills...). when sending a form it's goes in two table : Demande and Student.

Demande and Student = has many Skills = many to many

the 3 Tables are in a classic relation ship

class Demande extends Model
{
    ...
    public function student()
    {
        return $this->belongsTo(Student::class);
    }

    public function skills()
    {
        return $this->belongsToMany(Skills::class)->withTimestamps();
    }
    ...
}

class Student extends Model
{

    public function demandes()
    {
        return $this->hasMany(Demande::class);
    }

    public function skilles()
    {
        return $this->belongsToMany(Skills::class)->withTimestamps();
    }
}

class Skills extends Model
{
    public function demandes()
    {
        return $this->belongsToMany(Demande::class)->withTimestamps();
    }
}

I would like to retrieve old values in my form and at the same time recovers in edit page recover the data stored in the database.

here is my code:

    <div class="row checkbox-offres">
      <legend class="fieldset-label">Skills&nbsp;:</legend>
      @foreach ($skills as $skill)
      <div class="form-group-lg col-lg-6">
        <label>
          <input class="form-check-input @error('skills') is-invalid @enderror" type="checkbox"
            name="skills[]" value='{{$skill->id}}' @foreach($demande->skills as $skill_chosen)
          {{ (is_array(old('skills')) && in_array($skill->id, old('skills'))) ? 'checked' : '' }}
          @endforeach
          > {{$skill->name}}</label>
      </div>
      @endforeach
      @error('skills')
      <div class="invalid-feedback d-block">
        {{$errors->first('skills')}}
      </div>
      @enderror
    </div>

this code doesn't recovers old values in the add form and doesen't recovers data stored in databse. but recover old in the edit id someone mistake a field it's weird.

normally if I do

 {{ $skill_chosen->id == $skill->id ? 'checked' : '' }}

it's retrieve data form database but i want the old to when a user miss the field.