Regarding change in temperature in Bomb Caloriemeter
Basically, a bomb calorimeter consists of a small cup to contain the sample, oxygen, a stainless steel bomb, water, a stirrer, a thermometer, the dewar or insulating container (to prevent heat flow from the calorimeter to the surroundings), and ignition circuit connected to the bomb. (*)

The whole device known as calorimeter consists of a bomb and a water bath, they are not two separate entities. So, $ C_{cal}$ is actually referring to the heat capacity required of the steel vessel and also the water. The construction of the calorimeter is such that the thermal mass of the calorimeter system completely absorbs the heat of reaction (**).

*: This Wikipedia
**: Refer 29:27 of this video