We measure the nuclear quadrupole resonance (NQR) signal on the Zn site in nearly optimally doped YBa$_2$Cu$_3$O$_{6.92}$, when Cu is substituted by 3% of isotopically pure $^{67}$Zn. We observe that Zn creates large insulating islands, confirming two earlier conjectures: that doping provokes an orbital transition in the CuO$_2$ plane, which is locally reversed by Zn substitution, and that the islands are antiferromagnetic. Also, we find that the Zn impurity locally induces a breaking of the D$_4$ symmetry. Cluster and DFT calculations show that the D$_4$ symmetry breaking is due to the same partial lifting of degeneracy of the nearest-neighbor oxygen sites as in the LTT transition in La$_{2-x}$Ba$_x$CuO$_4$, similarly well-known to strongly suppress superconductivity. These results show that in-plane oxygen $2p^5$ orbital configurations are principally involved in the metallicity and superconductivity of all high-T$_c$ cuprates, and provide a qualitative symmetry-based constraint on the SC mechanism.
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