Is this what you are looking for?
file_url($uri)
This helper function accepts a relative path from the root and creates an absolute path to the file.
{{ file_url(node.field_example_image.entity.uri.value) }}
https://www.drupal.org/node/2486991
Edit:
Your PHP from your latest edit would translate into twig like this:
{{ node.field_my_link.0.url }} This works like this, 0 returns the first item of the field item list, url gets the url object and because twig will cast this object as a string this will call the magic method toString() and will output the url as a string value.
You only need to use url, because twig looks automatically for the method getxyz() if there is no property with that name xyz.