Apparently there are still pretty common Drupal 8 theming tasks that cannot be accomplished with the great twig_tweak module. This by the way was me giving a plug to a great little module, which makes half of all your theme preprocess hooks unnecessary.
Update: Apparently there is a module like twig_tweak but with the ability to do the above. It is called bamboo_twig and its documentation can be found here - thanks to Luckhardt Labs for mentioning it. Mind you I have not tested it yet. There is a rather interesting issue in its queue about the lack of collaboration between the two module maintainers.
If you would like to get the URL from an image that is trapped inside of a media entity however, you can either extract it using the aforementioned preprocess function like so: