Well think of it this way.
The bracket is bolted onto the head. The CAS is bolted onto this bracket by three bolts. The spindle from the CAS simply sits inside the exhaust cam and free spins as the camshaft rotates. Inside the CAS bolted to the shaft is a plastic like circle with 6 holes of different sizes that rotates through a measured point. This is how the CAS knows which cylinder to fire.
Now you said the bracket had snapped clean off, meaning there is nothing really holding the CAS in place other than the fact the bolts are holding it through the timing cover. There would be a lot more vibration coming through the spindle and possibilty of it starting to rotate off of its axis.
Add to the fact that you said the semi circle in the exhaust camshaft has now snapped leads to the fact it has been vibrating and putting stress onto the spindle.
So without seeing the car and only going off what you have said, I can assume that there is a high chance of the CAS being damaged in some way given how sensitive it is. Even a slight movement of it can throw the timing way out.
So without being dodgy the way to fix this properly is to get a new exhaust camshaft, a new CAS bracket and putting it all back together to see if it works. If it is still running rough than most likely the CAS is damaged and you will need a replacement of that aswell.