A search for the flavor-changing neutral-current decay $B^{+}\to
K^{+}\nu\bar{\nu}$ is performed at the Belle II experiment at the SuperKEKB
asymmetric energy electron-positron collider. The results are based on a data
sample corresponding to an integrated luminosity of $63\,\mbox{fb}^{-1}$
collected at the $\Upsilon{(4S)}$ resonance and a sample of $9\,\mbox{fb}^{-1}$
collected at an energy $60\mathrm{\,Me\kern -0.1em V}$ below the resonance. A
novel measurement method is employed, which exploits topological properties of
the $B^{+}\to K^{+}\nu\bar{\nu}$ decay that differ from both generic
bottom-meson decays and light-quark pair production. This inclusive tagging
approach offers a higher signal efficiency compared to previous searches. No
significant signal is observed. An upper limit on the branching fraction of
$B^{+}\to K^{+}\nu\bar{\nu}$ of $4.1 \times 10^{-5}$ is set at the 90%
confidence level.