The use of kelvin over Celsius has nothing to do with precision. They’re the same thing, with different offsets.
Technically yes and no. Kevin is absolute temperature, since the offset is zero it measures the total temperature. Celsius is relative, since the offset places its zero at a conventionally useful place it measures deviation from that baseline. That’s why you have temperatures always in K and never °K, but always in °C and never just C. But yes, the sizes of the units are the same.
Kelvin and Celsius can both be used interchangeably and you can always get the same answer every time using either; they are equally as precise. So is fehrenheit for that matter, although the conversion would get even more complicated.
It’s just usually using the one with zero offset makes the math easier, which is why it tends to be the one used for scientific calculations.
When the measurement being used is ∆T, change in temperature, this is correct. Occasionally, like in the ideal gas law equation, the measurement is T, or absolute temperature, which requires zero offset. In these cases, Celsius will give the wrong answer.