I was induced at 36weeks due to reduced movements so a bit sooner than you but literally had a sweep at about 6/7pm I was already 2cm dilated then about 8/9pm I had the pessary inserted , things moved fairly quickly for me and he was here the next morning. He did have to go to the nicu but he was younger so hopefully yours won’t but I will say I found induced labour a lot more painful than my natural birth I had🙈
With my second, I was induced at 40+6 for reduced movements. It took 4 attempts, but when I was in labour, it was fast. I had to spend every day in the hospital for a month beforehand to be on the monitor all day to make sure she was OK in there.