Laravel 9, Parent child bulk insert while replacing uuid to id

I have following table structure.

Table: movies

Table: categories

Table: movie_categories

POST: …/api/movies/create

{
  "title": "movie 2",
  "category_ids": [
    "uuid-c01",
    "uuid-c02"
  ]
}

Models/APIs/v1/Movie.php

class Movie extends Model {
    ...

    public function movieCategories() {
        return $this->hasMany(MovieCategory::class);
    }

    ...
}

Models/APIs/v1/MovieCategory.php

class MovieCategory extends Model {
    ...

    public function movie() {
        return $this->belongsTo(Movie::class);
    }
    public function category() {
        return $this->hasOne(Category::class);
    }
}

Models/APIs/v1/Category.php

class Category extends Model {
    public function movieCategory() {
        return $this->belongsTo(MovieCategory::class);
    }
}

Controllers/APIs/v1/MovieController.php

public function store(MovieRequest $request) {
    try {
        $Post = $request->validated();

        $Movie = Movie::create([
            'uuid'  => Str::uuid(),
            'title' => $Post['title'],
        ]);

        $Movie->movieCategories()->create($Post['category_ids']);

        ...
    } catch (Throwable $th) {
        ...
    }
}

Now, the question is that in the category_ids I am passing the uuids of categories, but in the movie_categories table the column is accepting the id of the categories table.

When I am running the code, I am getting the following error:

{
  ...
  "error": {
    "code": "22003",
    "message": "SQLSTATE[22003]: Numeric value out of range: 1264 Out of 
                range value for column 'category_id' at row 1 (SQL: 
                insert into `movie_categories` 
                (`movie_id`, `category_id`, `uuid`, `updated_at`, `created_at`) 
                values 
                (3, uuid-c01, uuid-string, 2025-04-01 07:36:18, 2025-04-01 07:36:18))"
  }
}

Whereas the output should be:

Table: movie_categories

I know that there are various other ways to achieve this, such as: Observers, MySQL triggers, Fetching ids before inserting, but I was wondering if there is more appropriate(Laravel based) solution this problem.