CoroutineRunner.cs

using System;
using System.Collections;
using System.Threading.Tasks;
using UnityEngine;

namespace Hoge
{
    public class CoroutineRunner : MonoBehaviour
    {
        private static MonoBehaviour instance;

        public static Task<T> Run<T>(Func<TaskCompletionSource<T>, IEnumerator> coroutine)
        {
            if (instance == null)
            {
                var go = new GameObject("CoroutineRunner");
                instance = go.AddComponent<CoroutineRunner>();
                DontDestroyOnLoad(go);
            }

            var taskCompletionSource = new TaskCompletionSource<T>();
            instance.StartCoroutine(coroutine(taskCompletionSource));
            return taskCompletionSource.Task;
        }
    }
}