Is there an uncertainty associated with the value 0 K for absolute zero?
As another answer explains, absolute zero is defined in the Kelvin temperature scale as precisely $\pu{0 K}$. But this is not the entire story, as all measurements have an associated uncertainty (all thermometers are imprecise), see e.g. the wikipedia article describing the International Temperature Scale of 1990 and the Provisional Low Temperature Scale of 2000. For instance the second wikipedia article links to a International Committee for Weights and Measures' document describing the uncertainties associated with the calibration of the temperature scale based on measurements of the melting pressure of $\ce{^3He}$.
Recently the SI value of the Kelvin was changed. This is explained in the wikipedia:

The definition of the kelvin underwent a fundamental change. Rather than using the triple point of water to fix the temperature scale, the new definition uses the energy equivalent as given by Boltzmann's equation.
Previous definition: The kelvin, unit of thermodynamic temperature, is 1/273.16 of the thermodynamic temperature of the triple point of water.
2019 definition: The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be $1.380649×10^{−23}$ when expressed in the unit $\pu{J⋅K−1}$, which is equal to $\pu{kg⋅m2⋅s−2⋅K−1}$, where the kilogram, metre and second are defined in terms of h, c and $\Delta ν_{Cs}$.
The kelvin may be expressed directly in terms of the defining constants as:
$$\pu{1 K} =  \frac{1.380 649 \times 10^{23}}{(6.626 070 15 \times 10^{-34})(9 192 631 770)} \frac{h \Delta \nu _{Cs}}{k}$$

So what does this mean for the definition of $\pu{0 K}$ ? That doesn't change, that is an absolute, thermodynamic definition. However, evidently the triple point of water is now no longer exactly $\pu{273.16 K}$. You can think of this as shifting the uncertainty from the size of a step to the number of steps that take you from absolute zero to the triple point. But both before and after the redefinition, $\pu{0 K}$ has meant $\pu{0\pm  0 K}$, that hasn't changed.

$^\ast$you can't actually reach absolute zero, so you can only extrapolate to 0 K and provide an uncertainty for this extrapolation, i.e. you could estimate how far your measured temperature is from absolute zero, and provide uncertainties associated with your estimate.