I always leave my phone and laptop off when going through TSA or Passport Control. I don't think in the US you an be compelled into giving up your password. They are free to confiscate the device but with it powered down good luck trying to break the password.
Powering down or restarting is ideal because BFU is much more secure.
Although, based on the latest Cellubrite leaks, GrapheneOS can't be exploited in AFU either.
There's also the reboot timer which brings the device to a BFU state. GrapheneOS implemented it and then Google and apple implemented their own version with fixed timers. GrapheneOS's is configurable down to 10 minutes, the default is 18 hours. On iPhones and Androids it's fixed at 72 hours.
One thing I wish they had in GrapheneOS was a faster shortcut to shutdown. Afaik currently you need to press physical button and then confirm on screen.