This looks quite interesting! My only concern with something like this is in a larger company that employees over 250+ developers (where I work), it appears to give too much "control" to the end user (the developer).
What's to stop, let's say, 25 different developers to doing a backup\restore at the same time? Or is there a way to manage who is able to do this? I looked at your provided images\gifs of how it works and I am quite intrigued by how it looks and functions.
I am a DBA that morphed into a part time developer with the creation of my webapp as well. The monitoring of the backup\restores to the end user is the primary focus of my webapp and is very helpful to my company.
I'll have to look more deeply into your web app to see how it works and if it's something feasible that could be incorporated into what I'm working on. My fear is eliminating the DBA entirely from the backend and as I mentioned before, giving too much control to the end user.
Nonetheless....very good! Thanks for posting this.