you can solve this problem in two ways, 1) set & 2) dispatch. Let's see,

Set

class Category extends Component
{
    public string $categoryId = "null";
    
    public function render()
    {
        return view('livewire.category');
    }
}

<div wire:ignore>
  <label>
    Category
  </label>
  <select
    name="category_id"
    id="category_id"
    wire:model="categoryId"
    data-control="select2"
    data-placeholder="Select a Category..."
  >
    <option value="">Select a Category...</option>
    <option value="1">Apple</option>
    <option value="2">Oppo</option>
    <option value="3">Vivo</option>
  </select>
</div>

<script>
  document.addEventListener('livewire:init', () => {
      $('#category_id').on('select2:select', function (e) {
          let value = $(this).val();
          @this.set('categoryId', value);
      });
  });
</script>

now if you change the select2 option the value will update. you can do this another way by using dispatch. Let's see

Dispatch

use Livewire\Attributes\On;

class Category extends Component
{
    public string $categoryId = "null";
    
    #[On('category-id')]
    public function updateProduct($category_id = null): void
    {
        $this->categoryId = $category_id;
    }
    
    public function render()
    {
        return view('livewire.category');
    }

}

<div wire:ignore>
  <label>
    Category
  </label>
  <select
    name="category_id"
    id="category_id"
    wire:model="categoryId"
    data-control="select2"
    data-placeholder="Select a Category..."
  >
    <option value="">Select a Category...</option>
    <option value="1">Apple</option>
    <option value="2">Oppo</option>
    <option value="3">Vivo</option>
  </select>
</div>

<script>
  document.addEventListener('livewire:init', () => {
      $('#category_id').on('select2:select', function (e) {
          let value = $(this).val();
          //@this.set('categoryId', value);
          Livewire.dispatch('category-id', { category_id: value });
      });
  });
</script>

I hope this will help you to solve your problem.

Note: use wire:ignore in the select2 root div otherwise it will disappear when you submit the form.