Last time it was all a bit of a mess. Placenta detached but membranes all tangled up inside me. Had to have a good fish around. MW was hopping about as she couldn't see what was going on with me being in the pool, but to her credit she asked me to explain what I could feel and gave me some guidance.
I had a natural 3rd stage - it took a while (about an hour) and I had to push in the end and to be frank finding the energy to push at that stage was hard! They had to empty my bladder first, I couldn't wee by myself and apparently that might have been obstructing it. (I hope I remember that right, I was fairly out of it with exhaustion.) I heard the injection can make you a bit sick and you are more likely to have heavy bleeding for the next few weeks. i was at home for my birth so in no rush, I thought I'd see if it came out naturally, which it did.
I had a natural third stage with both my sons, at my request. It gave me time to adjust to it all being over, havea a little talk to DH and a cuddle with baby and then DH got to cut the cord, which is an important beginning of fatherhood ritual to us.