We fit three more MTPs at the same accuracy level (i.e., same MTP hyperparameters, cf. SI) and based on exactly the same training set as used before, the only difference being that this training data is now computed with the pure PBE and rSCAN functional, as well as at the PBE+TS dispersion-corrected level. In the following, the newly trained ML potentials are denoted as MTP@PBE, MTP@PBE+TS and MTP@rSCAN, and we expect them to each be equally representative of the DFT functional used for their training data. On the one hand, the resulting series thus allows to compare two popular semi-local functionals (PBE and rSCAN) which are known to under-and overbind Cu in the solid state (see below), respectively. On the other hand, it allows for an evaluation of the influence of varying dispersion corrections, ranging from PBE with no dispersion, over PBE+TS which includes pairwise-additive dispersive Cu-C and C-C interactions, to PBE+MBD which includes many-body dispersive interactions among all species . , but for the different ML potentials, see text.