In Kontsevich's *Deformation quantization of Poisson manifolds*, he gives an explicit formula for the star product:
$$
f \star g = fg + \sum_{n=1}^\infty \hbar^n \sum_{\Gamma \in G_n} w_\Gamma B_{\Gamma} (f, g) \tag{$\ast$}
$$
where $B_\Gamma (f, g)$ is the bilinear operator associated to a graph $\Gamma$ and $w_\Gamma$ is a "weight", constructed as the integral of some configuration space.

I understand that the generalization of Kontsevich formality to the algebraic setting (smooth algebraic variety, possibly non-affine) is more involved and I have the following questions:

Is the formula for the weights in the (complex) algebraic context exactly the same as in the real and smooth case?

Are the weights computed "globally" or chart-by-chart, so that one has to check compatibility/gluing in an additional step?