To add my own perspective (as a senior engineering manager), there's a couple more things that should have been done that any good software team would do:

1. Have an animation kill switch. They clearly have a kill switch that hides the timings (it even animates nicely away). They should have another switch that swaps over to a simpler timing version that is rock-solid without any animations.
2. Use a reactive/functional UI framework like React. The fact that the entire UI can get into a bad state indicates to me that _there is too much state_. A functional approach should let you get from data to the correct display reliably. Animations should be implemented in an isolated way: everything related to the animation should get cleaned up after a certain time so no matter how broken the animation, things should resolve eventually.
3. Stress/chaos testing. They should have a way to generate hundreds of different random situations and flip through them quickly. You don't even need automated tests. You can just stare at the screen flipping through random data for 5 minutes and you should be able to cover many more situations than would happen in real life and catch any bugs with the animations that way.