G.♣.
My oldest was a little more than 2 1/2 when baby brother was born. We kept him company most of the time, but I did have to get up and leave occasionally. The door was always open, and I talked to him the whole time.
I really didn't leave until little brother was big enough (probably 3). The door was still open all the time, and I could hear them and talk to them. I tend to hover much more now, but that's because they tend to get roudy and get water all over the place if I don't supervise.
I really think so much of it depends on whether or not you can "leave" and still be very close and within ear shot. I would never be more than a room away, and I would be able to hear them. My boys tend to be very loud and very - energetic. If they quiet down even a little bit, I ask both of them to say, "Hi Mommy."
I think there is a way for you to give them some independence and still keep them safe.