Co-sleeping with cats + baby

My two cats, Miah & Suzi co-sleep with us. If we lock the bedroom door they cry at the door. I’m wondering how to handle this when the baby comes. I am 34w4d expecting our first child. Our baby will sleep with us in a bassinet beside the bed. The bassinet I bought has a zipper net on top, so that the cats can’t get to baby. I specifically bought that one so that my super cuddly cats don’t sit on him. One of the cats is a fat cat who doesn’t realize she is fat 😅 I have the bassinet out for the cats to explore. I don’t know what is the best approach with sleeping situation. Do I ban the cats from our room for the first few months? Or do I use the net and allow the cats to continue sleeping with us? I do not feel comfortable having the bassinet open and the cats sleeping in the same room until the baby is a few months old. What did you do?