The Belle and Belle II experiments have collected a $1.6\,\mathrm{ab}^{-1}$ sample of $e^+e^-$ collision data at center-of-mass energies near the $\Upsilon(nS)$ resonances. We conduct searches for transitions from the spin-singlet $h_b(1P,2P)$ states to the spin-triplet $\Upsilon(1S)$ and $\chi_{bJ}(1P)$ states. We do not find evidence for the $h_b(1P,2P)\to \Upsilon(1S) \pi^0$ and $h_b(2P) \to \chi_{bJ}(1P)\gamma$ transitions. We find the first evidence for the $h_b(2P)\to \Upsilon(1S)\eta$ transition. However, the measured branching fraction is lower than expected from related decays. Furthermore, we find evidence for $P_{c\bar c s}(4459)^0 \to J/\psi \Lambda$ decays in inclusive $\Upsilon(1S,2S)$ decays. This is the first evidence for an exotic state produced in $\Upsilon(1S,2S)$ decays.