However, achieving low error rates for fast two-qubit gates remains challenging, as suppressing leakage and non-adiabatic errors typically requires specialized qubit, coupler, or pulse designs, often at the expense of an idling ZZ=0 condition. In this work, we demonstrate that a symmetric floating tunable coupler provides a natural platform for fast, high-fidelity adiabatic controlled-Z (CZ) gates. Its favorable energy-level structure eliminates the conventional trade-off between rapid conditional-phase accumulation and adiabatic evolution while preserving exact cancellation of residual ZZ interaction at idling. This architecture exhibits intrinsic robustness to non-adiabatic transitions, even under simple flux modulation waveforms. To push performance at short gate durations, where maintaining adiabaticity becomes more challenging despite the favorable level structure, we introduce pulse-shaping techniques based on the instantaneous adiabatic factor that further suppress non-adiabatic errors. We experimentally realize a 24 ns adiabatic CZ gate with fidelity exceeding 99.9% and stable operation over several hours.