  We determine the branching fractions ${\mathcal{B}}$ and $CP$ asymmetries
${\mathcal{A}_{{\it CP}}}$ of the decays $B^+ \rightarrow \pi^+ \pi^0$ and $B^+
\rightarrow K^+ \pi^0$. The results are based on a data set containing 198
million bottom-antibottom meson pairs corresponding to an integrated luminosity
of $190\;\text{fb}^{-1}$ recorded by the Belle II detector in energy-asymmetric
electron-positron collisions at the $\Upsilon (4S)$ resonance. We measure
${\mathcal{B}(B^+ \rightarrow \pi^+ \pi^0) = (6.12 \pm 0.53 \pm 0.53)\times
10^{-6}}$, ${\mathcal{B}(B^+ \rightarrow K^+ \pi^0) = (14.30 \pm 0.69 \pm
0.79)\times 10^{-6}}$, ${\mathcal{A}_{{\it CP}}(B^+ \rightarrow \pi^+ \pi^0) =
-0.085 \pm 0.085 \pm 0.019}$, and ${\mathcal{A}_{{\it CP}}(B^+ \rightarrow K^+
\pi^0) = 0.014 \pm 0.047 \pm 0.010}$, where the first uncertainties are
statistical and the second are systematic. These results improve a previous
Belle II measurement and agree with the world averages.
