What happens if some anomaly happens where the shuttle loses power for a second?

Are you asking about what happens if all the power goes out or are you asking how they get state back? If everything reboots it’s fine. On restart the computers will look at all the sensors add project the state of now. There is no reason to keep the state of the past is there? Why does it matter where the craft was 5 minutes before? What matters is what is what is in front of them and the future right? If you tell the computer I want to fly home it looks at where you are and tells you how to get there. It does not need to remember the past parts of the trip does it?

It'd have to know that it's destination was earth, or does it just sit idle after a power on and wait for the command? What happens if the astronauts are asleep? I feel like it needs some persisted data.

I'm reminded of the quote from Linus:

"Real men don’t use backups, they post their stuff on a public ftp server and let the rest of the world make copies."

Real programmers don't use persistent storage, they just rely on physical reality in general.