@Azadouhi
When you deleted the bassinet, did you have a baby in the household at the time? Did you have any babies in any household anywhere else in the save at the time you deleted the bassinet?
What I am thinking is that for all practical purposes, babies and bassinets are connected objects. Until a baby is aged up to toddler, it remains an object and becomes a sim on age up which breaks the connection between the two objects. The game does not allow you to move a baby to another bassinet. You are stuck with the one the baby is generated in until age up. Since the CC bassinet was a default replacement, then deleting the object with a baby still connected may have caused your babies to remain connected to the default replacement somehow and the game can't reestablish a connection with the game bassinet which is now blocking the game object. And worst case, it may have caused all babies still in your save that were generated using the default replacement object to disappear from your save since they aren't connected to the bassinet they were generated in when you go to live mode for the household. And it could potentially cause other problems.
So please check this. Do NOT do it in live mode. That might cause the babies to disappear which could lead to other problems. Do it by looking at the households in Manage Households. Just look at the family portraits there so see if there are any babies. Don't take them to CAS just yet. Because if that is the case and you have babies, there might be a way to fix it by moving the families out of their homes and then back in so it forces the game to generate new bassinets for the babies. Once the connections between the bassinets and babies are reestablished, then the game bassinet should show up in the catalog again.
If you have no babies, then it's something else. Since you''ve already repaired, have you tried starting a new game in a new The Sims 4 folder with no mods and CC in it to see if the game bassinet is there?
Hope this helps.