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For moiré bilayer TMD superlattices, full-configuration-interaction (FCI) calculations are presented that take into account both the intra-moiré-quantum-dot (MQD) charge-carrier Coulombic interactions, as well as the crystal-field effect from the surrounding moiré pockets (inter-moiré-QD interactions). The effective computational embedding strategy introduced here allows for an FCI methodogy that enables the complete interpretation of the counterintuitive experimental observations reported recently in the context of moiré TMD superlattices at integer fillings ν=2 and 4. Two novel states of matter are reported: (i) a genuinely quantum-mechanical supercrystal of sliding Wigner molecules (WMs) for unstrained moiré TMD materials (when the crystal field is commensurate with the trilobal symmetry of the confining potential in each embedded MQD) and (ii) a supercrystal of pinned Wigner molecules when the crystal field is incommensurate with the trilobal symmetry or straining of the whole material is involved.

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