  The study of the rare decays $B\to K^{(*)} \nu \bar\nu$ offers a window into
the dynamics operating at the electroweak scale, allowing studies of the
Standard Model and searches for heavy new physics. However, the analysis of
these decays is also potentially sensitive to the on-shell production of new
light bosons $X$ through the process $B\to K^{(*)} X$. In particular, Belle~II
has recently measured $B^+\to K^+\nu\bar\nu$, finding a $2.8\sigma$ excess
under the assumption of heavy new physics. Since this excess is rather
localized in the kaon energy, a fit that includes the decay mode $B^+\to K^+ X$
to the kinematic distributions prefers $m_X\approx2\,$GeV with branching
fraction Br$[B\to KX]=(8.8\pm2.5)\times 10^{-6}$ and a significance of
$\approx3.6\sigma$. However, no excess was found in the BaBar measurements of
$B\to K^{(*)} \nu \bar\nu$, and a global analysis of the Belle II and BaBar
data leads to Br$[B\to KX]=(5.1\pm2.1)\times 10^{-6}$ with a reduced
significance of $\approx2.4\sigma$. We then study various simplified
dark-flavoured models and present a possible UV completion based on a gauged
$B_3-L_3$ symmetry, highlighting the discovery potential of dedicated searches
for $B\to K^{(*)}X$ at Belle II.
