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
No need to invoke metaphysics here. Whether time is an illusion or not doesn't depend on its "existence," though I'm not sure what you mean by "exists." I'm not convinced anyone does.
I agree with your overall point though. All we really need to say, when we say something is an "illusion," is that the phenomenon in question is not as it intuitively appears. Our expectations were one thing, but because of x, y, and z, this can't be the case. We think of it one way, but it's actually another way.
It's tempting to draw this distinction upon metaphysical lines, e.g., we thought it was one way, but here's how it Really (TM) is. Again, this is totally unnecessary and adds nothing to our scientific understanding.
So don't worry everyone time still exists.