See what being active on this thread has done- brought the graduates back to have a nosy! I was also an early grad and also wanted to congratulate Euro... yay! It sounds as if they are taking good care of you and they always err on the side of caution, so it sounds like you should be fine. Congratulations to everyone else as well, although I probably left the thread before your time, but if any have been here from the start and NCed, then special congratulations to you as well.
Both (yes both) mine were born at 37ish weeks by planned section (DD started to come a few days before the planned date so was technically emergency, but not really). It is really not much fuss and although I might complain slightly about the scar, if asked, 7months after number 2, I do remember thinking when DD was about one than I hadn't even thought about it for ages and all traces of an overhang had disappeared while I wasn't paying attention. My insurance didn't care if I drove after and I could easily lift a 22 month old after a week. By week three I had forgotten about it (and I had had a few complications due to my medical history).
It also doesn't feel like other hospital stays, more like a sleep over crèche. People are healthy and nurses just have nice supportive chats with you and coo over the babies instead of being rushed off their feet, patients worried and elderly and confused people waking you in the night to tell you there is an air raid. Honestly, it is so much nicer than other hospital stays you will have had!
Congratulations again and best of luck whatever you decide!