How I can search in database for a category given in url?

Upon development I want to reindex only specific categories because reindexing takes too long.

Therefore I am whipping a quick commang where I need to provide a category url and from that triggerring via object manager the reindexing of products and anything else required for this particular category.

namespace PcmagasTasksConsoleCommand;

use SymfonyComponentConsoleCommandCommand;
use SymfonyComponentConsoleInputInputInterface;
use SymfonyComponentConsoleOutputOutputInterface;


class PartialCategoryReindexer extends Command
{

    public function __construct(ObjectManagerInterface $objectManager)
    {
        $this->objectManager = $objectManager;
        parent::__construct(null);
    }


    public function execute(InputInterface $input,OutputInterface $output)
    {
       $url = $input->get('url');
       $path = parse_url($url, PHP_URL_PATH);
    
       // Trigger reindex here
    }

}

But how I can search for categories based upon url?