The shifted-prime Erdős-Wintner law for primitive-root determinant densities: extremal order, dimension zero, and Fourier decay

For a prime $p$, let $c(p)=\frac{φ(p-1)}{p-1}\prod_{j\ge1}(1-p^{-j})$, the limiting density of matrices over $\mathbb F_p$ whose determinant is a primitive root. Its limiting law over the primes is a continuous prime-indexed Bernoulli product with support $[0,1/2]$, Hausdorff dimension zero, and van