Recovery speed depends a lot on your general health and fitness, in my case I was out of the hospital in 5 days and back to work in 3 weeks. The main source of pain of course is your broken sternum, when you cough, sneeze, laugh, but amazingly it starts healing fairly quickly, they will give you a pillow that you embrace everytime you need to sneeze, etc so that it dampens the effect of the strain on your chest, you will also get pain medication. I can tell you, they discovered my aneurysm after an MTB accident, I broke my leg and needed surgery, my open heart surgery was 3 months after my leg surgery (I did not want to wait so I had it as soon as feasible) the pain from my broken leg far exceeded the pain from the open heart surgery.
I know open heart surgery sounds scary, but it is nothing compared to a disecting aneurysm, think about it this way, you know you have it and can do something about it, you are one of the lucky ones, a lot of people don't get that chance. In my case, I'm not going to lie I was nervous before surgery, but the stress of knowing I had a ticking bomb in my heart far exceeded the stress of surgery, I wanted it done as soon as possible.
As others said, find a thoracic surgeon that is an expert on aneurysms, someone who does this often, and get the support of a good cardiologist, also someone who specializes on aneurysms, if possible it is better if they belong to the same team and communicate, it makes a world of difference. Talk to them about any fear you have, the recovery, the details of the surgery, anything that gives you doubt or fear, they will have the answers.
I hope everything goes well, and yes ask me any questions you want to ask me, that is what this forum is for, to give each other advice and support.