Hi. Thanks for asking.
Unfortunately, embed.files.gallery was strictly made for displaying files and images. There is no additional interface for upload or other file manager actions. To use file manager actions, you would need to use the Files Gallery either in an iframe or in a modal overlay. I know iframe is not elegant, but it would work.
As for future, I could consider adding basic file manager options into Embed, for example on right-click. However, one of the points of Embed, is to remove most of the interface of Files gallery and just insert the gallery items saemlessly into an existing website. We can't really inject sidebars and topbar controls inside a container element that belongs to another website with it's own CSS.