Bouncing an ellipse with gravity, velocity, and reflection within another ellipse

After seeing this a bunch of times on social media I decided to try and code my own to limited success.

https://www.tiktok.com/@jacksphysics/video/7305867733889977633

Every time I start to unpack the problem I realise that there are a bunch of subtle issues to solve that are actually much harder than they look. Perhaps you could give us some clue as to the underlying physics.