Lepton-flavor violation (LFV) in charged-lepton decays is negligibly small in the Standard Model (SM), arising only through neutrino-mass suppressed loops with rates proportional to the ratio $(m^2_{\nu}/M^2_{W})^2 \lesssim 10^{-50}$, and thus well beyond experimental reach. Any observation of a $\tau$ LFV decay would be an unambiguous sign of physics beyond the SM. The Belle II experiment at the SuperKEKB asymmetric-energy $e^+e^-$ collider, together with the Belle legacy sample, provides a uniquely clean environment and large data sets of approximately 1.3 billion $e^+e^- \to\tau^+\tau^-$ events for LFV searches. This contribution reports: the world-leading Belle~II search for $\tau^- \to \mu^- \mu^+ \mu^-$ using an inclusive untagged strategy; the first Belle+Belle~II combined search for $\tau^- \to \ell^- K^0_S$; Belle~II searches for $\tau^- \to e^{\pm}\ell^{\mp}\ell^-$; and searches for invisible pseudoscalar bosons produced in $\tau \to \ell \alpha$ decays at Belle and Belle~II.