How is heat capacity a path function?

Heat capacity is NOT a path function. It is a STATE function. It depends on the phase of the material, the temperature and the pressure. Usually heat capacity is known at some particular condition and then a calculation is required to estimate it at the condition of interest. Performing these calculations should always result in the same final value no matter the path you took to get to the value - hence it is a STATE function rather than PATH. Path functions would be things like WORK and HEAT (for which the state function "heat capacity" might be used in the calculations)