In my experience it helps a lot to not think of it as an interview, but as a chat with just another coworker, and get genuinely engaged in what’s being asked.

I interviewed in most FAANG and got offers by just really engaging with the interviewers. Especially the system design rounds I found very fascinating and I treated the interviewers as if they would be my peers, challenging them (positively) when appropriate, and quickly admitting a mistake I just made.