Hi.
I sometimes put DS into bed with us, but always on my side & I sleep with my arms around him & sligtly uncomfortable, so I know he's there when I'm asleep.

I think you should lock the cat out of where ever he is. I've heard of cats looking for a warm spot to sleep & snuggling up with a sleeping baby is warm, but not good for baby. You cat could smother him.

At 9 weeks he's still only new & still working things out. He prefers to sleep on your chest where he can smell you & hear your heart beat.

Do you still wrap him? They like to be wrapped pretty firmly so it feels like the womb.
Maybe you could try a baby hammock or swing & see if it helps?
My DS went through a growth spurt at about 10 weeks, so that might be why he's unsettled for now. Hopefully he'll settle down again in a few days.

Good luck & it will get easier. It might not feel like it after a few days without sleep, but it will.