@JenS16 I'm so sorry you're having such a worrying time! I haven't read the full thread, but I did also have an emergency section (late at night!) with DD.
There was a concern that she might need an immediate section at one point, and I was beyond terrified and questioned them so closely about how long it would take / priority etc. they told me that in that scenario, they can get the baby out within 15 mins - in a 'worst case scenario' they will put you under as you go and immediately remove the baby. Whilst that sounds beyond awful, it did reassure me that if it got serious, there was an immediate plan.
In the end, I had a failed induction (not sure if that's your scenario) and DD heart rate was too high. When they stopped my drip her heart rate came down, but my water was broken already and there is a maximum length of time before they must deliver. I wasn't an immediate emergency, but I needed the operation. I think mine took place within a few hours, I recall that my surgeon had to leave and let his assistant finish up because he (and the paediatrician) got pulled out at the end for a serious emergency.
What I took from all of that is that if they need to do it, they will do it, and they will prioritise the baby and you if the emergency is there.
However, I don't think reminding them about you or asking questions is at all the wrong thing - I found it really hard because you want to trust the doctors but also your baby is the most important person in the world to you and you want to make sure they get all the care they need.
If I were you, I'd ask the doctors everything you want to know. Why did they say 2-24 hours if they arent doing it in that time. What are the risks here? What do you need to look out for and be on high alert for? What's the plan if things get more serious - how fast can they deliver and where will they do it? Get as much info as you need, and keep asking until you are satisfied.
I'm sure the doctors know exactly what they are doing, but you may feel better if you know the 'worst case' plan to reassure you