  Exploring correlations between the CP asymmetries of $B^0_d\to\pi^0K_{\rm S}$
following from an isospin relation, we uncover new tensions with the Standard
Model in data for neutral $B\to\pi K$ decays. Should this intriguing picture
originate from New Physics, a modified electroweak penguin sector provides a
key scenario. It includes models with extra $Z'$ bosons, which offer attractive
ways to resolve anomalies in $B\to K^{(*)}\ell^+\ell^-$ measurements. We
present a new strategy to reveal the underlying physics, apply it to current
$B\to\pi K$ data, and discuss the excellent prospects for Belle II.
