  We report measurements of the branching fractions and direct $\it{CP}$
asymmetries of the decays $B^0 \to K^+ \pi^-$, $B^+ \to K^+ \pi^0$, $B^+ \to
K^0 \pi^+$, and $B^0 \to K^0 \pi^0$, and use these for testing the standard
model through an isospin-based sum rule. In addition, we measure the branching
fraction and direct $\it{CP}$ asymmetry of the decay $B^+ \to \pi^+\pi^0$ and
the branching fraction of the decay $B^0 \to \pi^+\pi^-$. The data are
collected with the Belle II detector from $e^+e^-$ collisions at the
$\Upsilon(4S)$ resonance produced by the SuperKEKB asymmetric-energy collider
and contain $387\times 10^6$ bottom-antibottom meson pairs. Signal yields are
determined in two-dimensional fits to background-discriminating variables, and
range from 500 to 3900 decays, depending on the channel. We obtain $-0.03 \pm
0.13 \pm 0.04$ for the sum rule, in agreement with the standard model
expectation of zero and with a precision comparable to the best existing
determinations.
