In Final Cut Pro (which a friend uses, I don’t know it myself) there is an effect “Keynote” that for instance makes it possible to move the video aside in a cool way - see attachment - to make place/space for a text message, greeting.
You could use GL transitions which are available by Elusien’s WebVfx framework (http://www.elusien.co.uk/shotcut/gl-transitions/index.html). It needs a few steps but it should not be too difficult. It certainly is not as easy as using a filter. I do not know if there is a transition which resembles the Final Cut Pro effect, but “cube” or “InvertedPageCurl” might be also a nice way.
Sauron made a video with all available GL transitions (GL Transitions made using Elusien's GL transitions overlay generator).
You do not get the exact same perspective and there is no border color, but you can put it on video track V2, and it will show V1 in the black area - could be a color or image clip.
Also, you can animate the effect to go from full frame to this perspective and back.