Don't link menu in the active page
In D8 the handling of active links is split between php and js, so that the menus can be cached independently from the page they appear on. A solution in php or twig is only possible when you switch off caching of menus, but this is not good for performance. So a better approach is probably in javascript.

Remove the link tag by selecting the links with the class is-active:

mytheme/js/remove-active-links.js

(function ($, Drupal) {

  'use strict';

  Drupal.behaviors.removeActiveLinks = {
    attach: function (context) {

      $(context).find('a.is-active').contents().unwrap();

    }
  };

})(jQuery, Drupal);


You need to define a dependency on the core active-link.js, which sets the class is-active, so that your js file runs later:

mytheme/mytheme.libraries.yml

remove-active-links:
  version: 1.x
  js:
    js/remove-active-links.js: { }
  dependencies:
    - core/jquery
    - core/drupal
    - core/drupal.active-link




Background information

The js code above is the most basic solution, but it loads jQuery also for anonymous traffic, which is not a problem if you already use it.

If you want to avoid jQuery see ActiveLinkResponseFilter, which is a response subscriber adding the class is-active for anonymous requests.

You can then alter the result in a custom response subscriber with a lower priority, similar to the js code above.