Here is the code for getting category by category URL key.

The module name is: Magemonkeys_Categorydata

Create a block file: Categoryurl.php

<?php
namespace  MagemonkeysCategorydataBlockIndex;

class Categoryurl extends MagentoFrameworkViewElementTemplate {
{
 protected $filter;
 public function __construct(
      MagentoCatalogBlockProductContext $context,
      MagentoCatalogModelCategoryFactory $categoryFactory,
      array $data = []
    ) {
     parent::__construct($context, $data);
     $this->categoryFactory = $categoryFactory;
 }
 public function getCategory($urlKey)
 {
   $categories = $this->categoryFactory->create()->getCollection()
             ->addAttributeToFilter('url_key', $urlKey)
             ->addAttributeToSelect(['entity_id']);
     return $categories;
 }
}

Now you can get category by using this function getCategory($urlKey) in your phtml file

$urlKey = 'bags';
$category = $this->getCategory($urlKey);
print_r($category->getData());

You can get an array of category data.