Add media library tab

I'm trying to make a new tab in the media library. I have found the function add_media_page which helps me add a page in the media menu to the left. How ever, this menu is not always visible, for example when i want to set a featured image for a post or page. I want my tab to be visible next to the tab "Media library". (on the tab row where there's now two tabs; "Upload files" and "Media library", I want to add a tab here).

How can i hook into that?