Is this regex rule valid for validating domain name in 2022?

That is good enough but not perfect. For example, it does not work for "my-school.edu.np".

Instead, you could use PHP's own filtering, combined with Laravel validation.

First create custom validation rule in Laravel. https://laravel.com/docs/9.x/validation#custom-validation-rules

<?php

namespace App\Rules;

use Illuminate\Contracts\Validation\Rule;
 
class ValidDomain implements Rule
{
    
    public function passes($attribute, $value)
    {
        return filter_var($value, FILTER_VALIDATE_DOMAIN, FILTER_FLAG_HOSTNAME)
          ? true
          : false;
    }
 
    
    public function message()
    {
        return 'The :attribute must be a valid domain.';
    }
}

Then you could validate with:

use App\Rules\ValidDomain;

$request->validate([
    'domain' => ['required', new ValidDomain, 'url', 'active_url'],
]);

The url and active_url is also explained in the doc. https://laravel.com/docs/9.x/validation

I have not tested the code above. But the gist is similar.