There seem to be two types of post editors inside WordPress.com. I don't know the official names for them, so please excuse my choice of names below.
- The "blog-level" editor, which you enter from within the Dashboard for your specific WordPress.com blog, and which is the "main" and full-fledged editor.
- The "WordPress.com-level editor", which you can enter while logged into WordPress.com (for example, when viewing the WordPress.com "Reader") after pressing the "New Post" button.
Your screenshot seems to be of the latter, after choosing the "Text" option in response to "What would you like to post?". It seems that this "WP.com-level editor" is rather limited. It does not have an "Add Media" button, and only allows one to upload new images, without allowing one to choose existing images from the Media Library or to specify a URL for an externally hosted image.
I suggest that you do not use this "WP.com-level editor", and only use the "main, blog-level" editor. This editor has an "Add Media" button, offering both an "Insert Media" option (from the Media Gallery), as well as an "Insert from URL" option. You seem to be looking for the latter.