How to escape markup with check_markup in a twig template?
This seems like something you could do in a preprocess function and create that variable. At that level, you can use check_markup to check it.

Be sure to see the two notes on the docs page:


  Note: Because filters can inject JavaScript or execute PHP code,
  security is vital here. When a user supplies a text format, you should
  validate it using $format->access() before accepting/using it. This is
  normally done in the validation stage of the Form API. You should for
  example never make a preview of content in a disallowed format.
  
  Note: this function should only be used when filtering text for use
  elsewhere than on a rendered HTML page. If this is part of a HTML
  page, then a renderable array with a #type 'processed_text' element
  should be used instead of this, because that will allow cacheability
  metadata to be set and bubbled up and attachments to be associated
  (assets, placeholders, etc.). In other words: if you are presenting
  the filtered text in a HTML page, the only way this will be presented
  correctly, is by using the 'processed_text' element.


Here is a similar question/answer (albeit from 2014) that may still apply.