Is there any way to use your logo image within Shotcut to create a transition like this? If not, does anybody have an idea where I could make such a transition?
The Corner Pin would have to be keyframed. There are tutorials on keyframing on YT.
Friendly tip: If you want to try and understand a transition that is quick paced like that one on YT, you can step through it with the , and . keys on your keyboard (keys < and >) on a British keyboard at least.
This allows you to step through, frame by frame.
The most freedom for 3d transitions with special effects you’ll have in any 3d animation software like blender, cinema4d or 3dmax for example. But these are MUCH more complicated to learn than Shotcut
so make yourself familiar with the size & position filters in shotcut and keyframe technique - you will come out with something similar but not just as fancy as in the example.