コールバック版

using Kogane;
using System;
using UnityEngine;

public class Example : MonoBehaviour
{
    private readonly Hoge m_hoge = new Hoge();

    private void Update()
    {
        if ( Input.GetKeyDown( KeyCode.Z ) )
        {
            Hoge( "AAA" );
        }
        if ( Input.GetKeyDown( KeyCode.X ) )
        {
            Hoge( "BBB" );
        }
        if ( Input.GetKeyDown( KeyCode.C ) )
        {
            Hoge( "CCC" );
        }
    }

    private void Hoge( string message )
    {
        m_hoge.Play( () => Debug.Log( message ) );
    }
}

public class Hoge
{
    private enum State
    {
        IDLE,
        PLAYING,
        COMPLETE,
    }

    private Action m_onComplete;
    private State  m_state;

    public void Play( Action onComplete )
    {
        if ( m_state == State.COMPLETE )
        {
            onComplete();
            return;
        }

        if ( m_state == State.PLAYING )
        {
            m_onComplete += onComplete;
            return;
        }

        m_state = State.PLAYING;

        m_onComplete += onComplete;

        CoroutineUtils.CallWaitForSeconds
        (
            3, () =>
            {
                m_state = State.COMPLETE;

                m_onComplete();
                m_onComplete = null;
            }
        );
    }
}

UniTask 版

using Cysharp.Threading.Tasks;
using System;
using UnityEngine;

public class Example : MonoBehaviour
{
    private readonly Hoge m_hoge = new Hoge();

    private void Update()
    {
        Process().Forget();
    }

    private async UniTaskVoid Process()
    {
        if ( Input.GetKeyDown( KeyCode.Z ) )
        {
            await m_hoge.Play( () => UniTask.Delay( 3000 ) );
            Debug.Log( "AAA" );
        }

        if ( Input.GetKeyDown( KeyCode.X ) )
        {
            await m_hoge.WaitForCompletion();
            Debug.Log( "BBB" );
        }

        if ( Input.GetKeyDown( KeyCode.C ) )
        {
            await m_hoge.WaitForCompletion();
            Debug.Log( "CCC" );
        }
    }
}

public class Hoge
{
    private enum State
    {
        IDLE,
        PLAYING,
        COMPLETE,
    }

    private State                   m_state = State.IDLE;
    private UniTaskCompletionSource m_source;

    public async UniTask Play( Func<UniTask> action )
    {
        if ( m_state == State.COMPLETE )
        {
            Debug.Log( "完了済み" );
            return;
        }

        if ( m_state == State.PLAYING )
        {
            Debug.Log( "完了待ち" );
            await m_source.Task;
            return;
        }

        m_state = State.PLAYING;

        if ( m_source == null )
        {
            m_source = new UniTaskCompletionSource();
        }

        Debug.Log( "開始" );

        await action();

        Debug.Log( "完了" );

        m_state = State.COMPLETE;
        m_source.TrySetResult();
    }

    public async UniTask WaitForCompletion()
    {
        if ( m_state == State.COMPLETE )
        {
            Debug.Log( "完了済み" );
            return;
        }

        if ( m_source == null )
        {
            m_source = new UniTaskCompletionSource();
        }
        
        Debug.Log( "完了待ち" );
        await m_source.Task;
    }
}