How long after a aneurysm surgery do you have to stay off work?

Depends. What kind of aneurysm and what surgery ? For open abdominal aortic surgery around six weeks , for endovascular stent graft one to two weeks.
Depends. There is no one size fits all answer for this. It depends completely on the location of the aneurysm, the extent of the surgery, etc. Your surgeon will discuss this at length both before and after your surgery.