How can I calculate the uncertainties in magnitude like the CDS does?
That is because what is measured is a flux and the flux errors are in the DR2 catalogue.
Since magnitudes are based on the logarithm of the flux, then there is no straightforward correspondence (although it matters little if the error bars are less than a few hundredths if a magnitude).
Simple error propagation formulae give
$$|\Delta G| \simeq \frac{2.5}{\ln 10} \left(\frac{\Delta f}{f}\right),$$
where $f$ is the flux in the G band.
This gives $\Delta G= 0.0023(1)$ for your example. Other algorithms give almost the same result, e.g. taking the average of the $\pm \Delta G$ from using $\pm \Delta f$ to calculate the magnitude.
If the difference between the algorithms (they do give differing results when the flux error exceeds $\sim 10$%), or the fact that the true error is asymmetric in magnitude are important, then you shouldn't be using the symmetric magnitude error bar from CDS.