Does NCL transfer our luggage to the ship so we can spend more time in the in San Fransico?

No! You'll have to pick up your bags at the airport.

I'm trying hard to figure out how NCL is going to pick up your bags and get them to the ship? Who is going to do it?

San Francisco isn't even a regular home port for NCL, and you're asking for a service they don't provide at their regular home ports.

Well Royal Carribean did so I didnt know because it is my first time on NCL.