That's a very good question. I started but abandoned a fairly deep answer, mostly because this is an area far from my expertise and in which it is easy to be howlingly wrong. (To be fair to me, subject matter experts have been arguing about this in the literature for some twenty years.)

Instead I'll direct you Sean Carroll's "Quantum Interrogation" blog posting as a starting point: <https://www.preposterousuniverse.com/blog/2006/02/27/quantum...>. ("how you can detect something without actually looking at it")

There is also the 2021 work by the Google & Stanford team (decent press release: <https://news.stanford.edu/2021/11/30/time-crystal-quantum-co...> open-access paper: <https://www.nature.com/articles/s41586-021-04257-w>, the PDF version of which (click in top right) is legible) which is at least suggestive that certain types of time crystals can be interrogated without breaking them.

Thank you! Reading it now!