We report updated measurements of branching fractions ($mathcal{B}$) and CP-violating charge asymmetries ($mathcal{A_{rm CP}}$) for charmless $B$ decays at Belle II, which operates on or near the $Upsilon$(4S) resonance at the SuperKEKB asymmetric energy $e^{+}e^{-}$ collider. We use samples of 2019 and 2020 data corresponding to 62.8 fb$^{-1}$ of integrated luminosity. The samples are analysed using two-dimensional fits in $Delta E$ and $M_{it bc}$ to determine signal yields of approximately 568, 103, and 115 decays for the channels $B^0 to K^+pi^-$, $B^+ to K_{rm S}^0pi^+$, and $B^0 to pi^+pi^-$, respectively. Signal yields are corrected for efficiencies determined from simulation and control data samples to obtain branching fractions and CP-violating asymmetries for flavour-specific channels. The results are compatible with known determinations and contribute important information to an early assessment of Belle II detector performance.