How important is cost estimation in system design interviews?

I've seen varying opinions on how important cost estimation is in system design interviews. Should you proactively bring up infrastructure costs, or only address them if the interviewer specifically asks? And if you do, how precise do those estimates need to be? My understanding is that for senior+ roles, demonstrating an awareness of cost implications is valuable. I usually try to include a quick, back-of-the-envelope calculation if the scale of the system is significant (e.g., 'With 100M users and X GB of data per user, storage costs would be in the range of Y per month on AWS S3'). I have a mental framework for ballpark AWS costs per GB, per million API calls, etc. Is this level of detail sufficient, or should I be prepared to break down costs more granularly (compute, network, storage, managed services)? Or is it often an unnecessary diversion from the core design problem? I'm trying to gauge the expectation here.