How to record the time of pressing the UI buttons, and repeat the press.

You just need variables to keep track of when you press buttons. I would probably put it all in a class. Like have an action class and then have a float timePressed in it. Then you can keep track of when every action was executed and you can make a recording of it by putting it in a list. Then you execute it based on your timePressed value.

I did. Algorithm: 1.add the desired button to the script 1. add her OnClick event with the desired method from this script 3.create coroutine in the script if it is not 2. call it a separate method by pressing

 using UnityEngine;
 using UnityEngine.UI;
 
 public class Click_tracking : MonoBehaviour
 {
     //массивы для записи времени нажатий каждой кнопки
     public float[] _time; public float[] _time1; public float[] _time2; public float[] _time3; public float[] _time4; public float[] _time5; public float[] _time6; public float[] _time7; public float[] _time8; public float[] _time9; public float[] _time10;
 
     public int[] _counts; //счётчики количества нажатий
     public Button[] _button;
 
     bool _cheakTimer = false;
     public float _timer; //таймер
 
     private void Update()
     {
         _timer += Time.deltaTime;
     }
 
     public void NewMethod() // методы для фиксации времени нажатий
     {
         if (!_cheakTimer)
         {
             _time[_counts[0]] = _timer;
             _counts[0] += 1;
         }
         Debug.Log(_button[0]);  
     }
 
     public void NewMethod1()
     {
         if (!_cheakTimer)
         {
             _time1[_counts[1]] = _timer;
             _counts[1] += 1;
         }
     }
    
     public void Reproduce() // метод для запуска корутин
     {
         _cheakTimer = true;
         _timer = 0.0f;
 
         StartCoroutine("Zero");
         StartCoroutine("First");
         StartCoroutine("Second");
        
         Debug.Log("Старт корутины");
     }
 
     public IEnumerator Zero() // корутины для вызова нажатий
     {
         for (int i = 0; i < _counts[0]; i++)
         {
             if (i == 0)
             {
                 yield return new WaitForSeconds(_time[i]);
                 _button[0].onClick.Invoke();
                 Debug.Log("Есть первое пробитие");
             }
             else
             {
                 yield return new WaitForSeconds(_time[i] - _time[i - 1]);
                 _button[0].onClick.Invoke();
                 Debug.Log("Есть второе пробитие");
             }
         }
 
     }
     public IEnumerator First()
     {
         for (int i = 0; i < _counts[1]; i++)
         {
             if (i == 0)
             {
                 yield return new WaitForSeconds(_time1[i]);
                 _button[1].onClick.Invoke();
                 Debug.Log("Есть первое пробитие");
             }
             else
             {
                 yield return new WaitForSeconds(_time1[i] - _time1[i - 1]);
                 _button[1].onClick.Invoke();
                 Debug.Log("Есть второе пробитие");
             }
         }
     }
     public IEnumerator Second()
     {
         for (int i = 0; i < _counts[2]; i++)
         {
             if (i == 0)
             {
                 yield return new WaitForSeconds(_time2[i]);
                 _button[2].onClick.Invoke();
                 Debug.Log("Есть первое пробитие");
             }
             else
             {
                 yield return new WaitForSeconds(_time2[i] - _time2[i - 1]);
                 _button[2].onClick.Invoke();
                 Debug.Log("Есть второе пробитие");
             }
         }
     }
     public IEnumerator Third()
     {
         for (int i = 0; i < _counts[3]; i++)
         {
             if (i == 0)
             {
                 yield return new WaitForSeconds(_time3[i]);
                 _button[3].onClick.Invoke();
                 Debug.Log("Есть первое пробитие");
             }
             else
             {
                 yield return new WaitForSeconds(_time3[i] - _time3[i - 1]);
                 _button[3].onClick.Invoke();
                 Debug.Log("Есть второе пробитие");
             }
         }
     }    
 }