Measurements of electroweak penguin and lepton-flavour violating $B$ decays to final states with missing energy at Belle and Belle~II

The Belle and Belle~II experiments have accumulated a data set of $1.2~\mathrm{ab}^{-1}$ of $e^+e^- \to B\bar{B}$ collisions at the $Υ(4S)$ resonance. Owing to the clean event environment and well-constrained initial-state kinematics, these data are ideally suited for searches for rare electroweak penguin and lepton-flavour violating $B$ decays with missing energy from neutrinos. We report results on $b\to sν\barν$ processes and the interpretation, together with searches for $B\to K^{*0}τ^+τ^-$ and for the LFV decays $B^0\to K_S^0τ^\pm\ell^\mp$ and $B^0\to K^{*0}τ^\pm\ell^\mp$ ($\ell=e,μ$).