We know how an "Add H5P" button should be included in the new editor of WordPress 5+ which has at least the same functionality as today's button, but could possibly be integrated more smoothly.
As of WordPress 5.0, the post editor will change. The current editor will be replaced by what today is the plugin plugin Gutenberg. The implementation can already be tested in the alpha version of WordPress 5.0 or by using the plugin.
While the H5P shortcode still works, the H5P button to include content is not being displayed in the Gutenberg editor. It should ideally be integrated as what's called a "block" in Gutenberg, cmp. the Gutenberg documentation. Some design work may be necessary.