Add Category Dropdown to Admin Filter

How can you add category dropdown to admin filter in WordPress? This use case shows how a focused WordPress code snippet can handle the task without installing a heavy plugin. The snippet should add category filter dropdown to a custom post type list and produce this result: Admins can filter custom post type entries by category. You can also log in to LeonLab.ai, describe this WordPress use case in plain English, generate the snippet, review the PHP code, and deploy it to the selected WordPress project.