Can Laravel do what WordPress does?

Yes, with deliberate effort. Laravel does not ship with WordPress's content management features out of the box, so you either build them, use Laravel based CMS packages (Statamic, Filament with admin extensions, October CMS), or run WordPress headless and consume its REST API from a Laravel application. Most teams migrating from WordPress to Laravel discover that they were using only 20 percent of WordPress's CMS features, and rebuilding that 20 percent in Laravel is a manageable effort that gives them the application flexibility they actually needed.