Cats being in baby's cribs

Hi guys so I this might sound dumb but I've been wondering about this since I'm over halfway through my pregnancy. So I have a cat he's absolutely my little baby and sleeps in my room all the time with me. He's very affectionate and will "headbutt/kiss" me through the night and sleep on my tummy or back, which is fine. I adopted him when I was 17, in grade 11 after having a miscarriage. I've had him for a long time. Now when I was in grade 11 I took the parenting course and had the robotic baby that cried all night and day lol. I had a car seat placed beside my bed for the baby to "sleep in". But whenever the baby cried throughout the night, my cat would run over and sit on the baby's stomach and just investigate or whatever he was doing. Since I'm pregnant now I'm worried he might do this to my real baby. I guess I'm asking if I should be worried about this and maybe not let him sleep in my room or my baby's room just in case. Could he actually hurt or sufffocate her? And why would he do this to the fake baby? I'm just worried and need some guidance