How can I add a tab to the admin/content page
Similar to Drupal 7, tabs are called "local tasks". Your module should implement a local task and a route.

The complexity in this is that /admin/content is a views-generated route with a system module fallback in case the view is disabled (as explained by @Berdir below), and the base route should be system.admin_content.

mymodule.mytask:
  title: 'My Task'
  route_name: 'mymodule.mytask.route'
  base_route: 'system.admin_content'
  weight: 1


If the view itself isn't altered, then the route is view.ID.page_NUMBER. I've done this latter thing working on an entity example module in my sandbox (Shift).