Electroweak penguin and lepton-flavour violating $B$ decays are key focuses of the Belle II physics program. These processes are particularly challenging due to the presence of neutrinos in the final states, resulting in `missing energy' in the rare $b\to s$ transitions. Using electron-positron collision data collected at the $\Upsilon(4S)$ resonance, we present the first evidence for $B^+\to K^+\nu\bar{\nu}$ decay and the most stringent upper limit on $B^0\to K^{*0}\tau^+\tau^-$ decay. Additionally, combining Belle and Belle II data, we report the first search on lepton-flavour violating $B^0\to K^{0}_S\tau^\pm\ell^\mp$ ($\ell=e,\mu$) decays.