There’s something else going on here. At the very beginning of your video, there’s a gap between the top bar where the buttons are and the rest of the modal. That is not there in a fresh ClassicPress install. So you need to identify what is causing that; it’s almost certainly the same thing that’s causing the issue you reported.
There are two possibilities. One is highlighted by the fact that you said that .edit-media-header is absolutely positioned. I don’t remember whether it was before, but it certainly is not in CP v2.3.1. So it’s possible you have a caching issue.
The alternative is that you have a plugin conflict. If you can rule out the caching issue, can you try deactivating all the plugins, clear caches again, and see whether the problem persists?
I’m hoping to work on the media widgets in the spring. If I can get that done (which I’d like to do by the summer) then it should be possible to rationalize a lot of the CSS on the media and widgets pages so that adjustments like this will then no longer be needed.