Nilpotent descent under fpqc covers for morphisms of stacks

Ascertain whether Theorem 6.*(3) (that a nilpotent extension f: Y → X of quasi-geometric stacks induces a weak nilpotent extension Perf(X) → Perf(Y)) remains valid when replacing quasi-affine fpqc covers by general representable faithfully flat covers. In other words, determine if the nilpotent-extension conclusion descends under fpqc covers in this greater generality.

Background

Theorem 6.*(3) proves that for quasi-affine morphisms the pullback on perfect complexes is a weak nilpotent extension of c-categories.

The authors extend parts (1)–(2) beyond quasi-affine covers, but their proof of (3) relies on quasi-affineness, and they do not know if (3) holds under merely representable faithfully flat covers.