1. Store a in a field.
2. Call any of the methods before playing a new animation.
3. Then call any of the methods after playing the animation.

// 1. Define your group type.
// You could use strings or ints or whatever you want, but enums are often best.
public enum AnimationGroup
{
    None,
    Movement,
}

[SerializeField] private AnimancerComponent _Animancer;

// 2. Store a TimeSynchronizer in a field.
private readonly TimeSynchronizer<AnimationGroup>
    TimeSynchronizer = new();

public AnimancerState Play(AnimationClip clip, AnimationGroup group)
{
    // 3. Call one of the StoreTime methods before playing a new animation.
    TimeSynchronizer.StoreTime(_Animancer);
    
    // 4. Play an animation.
    var state = _Animancer.Play(clip);
    
    // 5. Call one of the SyncTime methods after playing the animation.
    // If the `group` was the same as the value from last time you called it,
    // then the state's NormalizedTime will be set to the stored value.
    TimeSynchronizer.SyncTime(state, group);
    
    return state;
}