Gregory's Server
To achieve this, there are 2 changes needed for View Transitions:
1. A view-transition-group property to determine where to place the snapshot.
2. [experimental] A new capture mode that copies over certain properties (clip-path, border-radius, opacity, …) to the ::view-transition-group()
Combine the two, and you get what you see in that second recording there :)
Note that new capture mode is something experimental that Chrome is exploring. If all goes well this new mode will eventually replace the old one because it has much nicer results.