I have seen it expressed that for the quadratic form;
$$ ()=^T+^⊤+ $$
for symmetric $A$, and where $x$ follows multivariate normal,
$$ ∼N(,Σ), \quad ^⊤=. $$
then, $$ Var[()]=2Tr(ΣΣ)+4^⊤Σ+4^⊤Σ+^⊤Σ $$
But I'm struggling to find a publication that contains the proof as a citation. Can anyone help?