It seems like there is only opT["I",{2,0}] in your Hamiltonian:

HQ[\[CapitalOmega]_]:=Simplify@ExpToTrig[\[Omega]Q*{-\[Eta]Q/Sqrt[6],0,1,0,-\[Eta]Q/Sqrt[6]}.WignerD[2,{{0}}][\[CapitalOmega]]*opT[I,{2,0}]/Sqrt[6]];

Shouldn't opT["I",{2,0}] be a matrix of {opT["I", {2, -2}], opT["I", {2, -1}], opT["I", {2, 0}], opT["I", {2, 1}], opT["I", {2, 2}]}? This is so that the components of the Wigner matrix will multiply by their respective tensor operators.

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