You shouldn't take 'Illusion' too strongly here. Ms Hossenfelder is saying that conceptually time can't really be separated from 'change' so the only way to measure time is to have some constantly changing but steady ticker like a pendulum. This has always been a problem in quantum mechanics because you can't study the a system independently of its clock, you have to add the clock to the system. The video is discussing a paper where they use entanglement and a tiny ticker to get around this problem. Arxiv: https://arxiv.org/abs/2310.13386

So don't worry everyone time still exists.