  We report updates on time-dependent $CP$-violation observables at Belle II.
The benchmark measurements of the $B^0$ lifetime $\tau_{B^0}$ and mixing
frequency $\Delta m_d$ using flavor specific hadronic decays and the
determination of the $CP$-violating phase $\sin2\phi_1$ in $b\to
c\overline{c}s$ transitions have been performed using data collected between
2019-2021. These analyses use only half of the current available dataset and
are still statistically limited, showing the excellent performance of the
detector and readiness of the analysis tools. We present three new results on
the effective value of $\sin2\phi_1$ in $b\to q\overline{q}s$ transitions,
which are highly sensitive to generic non-Standard Model (SM) physics
amplitudes, using the full dataset collected between 2019-2022.
