This will sound nuts to some I am certain, but I did not push- at all with either of my daughters. My body literally expelled them from my body, and no effort was required of me other than being a part of the process. Both were vaginal, drug free midwife assisted births. 3 hours of labor for the first and then 2 hours of labor. But I did nothing but hand myself over to the process... it sounds crazy even now. But I never pushed at all.
On my fifth baby I studied unassisted birth voraciously just to learn what it was supposed to be like when no one interfered or coached. I read hundreds of stories. Many, even a majority of the moms described delivery just like you did. It isn't crazy at all. It is what can often happen when a birthing mother is undistracted by her birthing assistants. In my first four births I had never felt a "pushing contraction", it was always transition and then my body quit. The pushing phase always took FOREVER with me doing all the work. I realized that hospital staff had made me wait too long to push with every birth. Those really hard to deal with contractions that came at about 8cm…that is when I should have pushed because those contractions were powerful and they would have gotten the baby out efficiently. When I felt those huge contractions with my fifth baby the nurse said I was 5-7cm. I pushed, very slightly, through each contraction from then on and I felt my body do all the rest of the work. My baby was born with very little effort from me an hour later. My main job was major pushing the last two minutes when the shoulders got stuck.