  The formula $\star$ mod $\bar{o}(\hbar^k)$ of Kontsevich's star-product with
harmonic propagators was known in full at $\hbar^{k\leqslant 6}$ since 2018 for
generic Poisson brackets, and since 2022 also at $k=7$ for affine brackets. We
discover that the mechanism of associativity for the star-product up to
$\bar{o}(\hbar^6)$ is different from the mechanism at order $7$ for both the
full star-product and the affine star-product. Namely, at lower orders the
needed consequences of the Jacobi identity are immediately obtained from the
associator mod $\bar{o}(\hbar^6)$, whereas at order $\hbar^7$ and higher, some
of the necessary differential consequences are reached from the Kontsevich
graphs in the associator in strictly more than one step.
