Time-dependent $CP$ violation results at Belle II

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.