Counterpoint to this...I like the idea of the Jedi doing all the menial work as well. Tend gardens, maintain buildings and equipment, etc...b/c it shows they are also willing to do the work that everyone else has to as well.
Eventually, but the movements of the Death Star were closely guarded, and it left pretty quickly afterwards to chase the rebel base.
There's time for a LOT of people and equipment to get relocated.