We don’t usually even thinking about getting a new cat for several months after one dies. We recently had our youngest (3 years) get knocked over on the road and this is the first time that we’ve ever considered “replacing” a cat because our 5 year old missed her so much that she became Ill with the stress.
She’s ok now but she’s a lot more clingy than she used to be.
I hope you find your other cat. We know someone who lost theirs and found him after what must have been six months so there’s always a chance.