TaskCompletionSource を使用する

Timelineを再生し終了するまでのTask

public async Task ShowAhimAsync(CancellationToken token = default)
    {
        var tcs = new TaskCompletionSource<int>();

        System.Action<PlayableDirector> handler = null;
        handler = (obj) =>
        {
                playableDirector.stopped -= handler;
                tcs.SetResult(0);
        };
        playableDirector.stopped += handler;

        playableDirector.time = 0;
        playableDirector.Play(showAsset, DirectorWrapMode.None);

        using(token.Register(() =>
        {
            // キャンセル発生時の処理
            playableDirector.stopped -= handler;
            tcs.SetCanceled();
        }))
        {
            await tcs.Task;
        }
    }