The implemented solution does not work when changing the theme to e.g. "clean". It seems the theme is responsible for rendering the DOM as well, not only styling.
Created a new commit, where the old solution is used for all themes, except Boost, which bugged out (as we remember). The Boost theme now gets a html-field rendered as a single element, inside a group, with a label.
Note that the group field, with the html field inside doesn't work for all other themes, so it can't be a replacement for all themes.
There also isn't any markup rendered anymore by our code.
H5P file upload is shown always (i.e. also if "create" is selected)