How can I start countdown after OnTriggerEnter2D and change bool check to false

using System;
using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class TripleShot : MonoBehaviour
{

    public static bool check;

    public void OnTriggerEnter2D(Collider2D col)
        {
            if (col.tag == "Player")
            {
                Destroy(this.gameObject);
                SoundManager.instance.Play(SoundManager.SoundName.tripleShotCollect);
                check = true;
                StartCoroutine(tripleShotTimer());
            }
        }
    IEnumerator tripleShotTimer()
    {
        yield return new WaitForSeconds(10f);
        check = false;
    } 
}

In order for a collision to happen, you need a BoxCollider2D with Is Trigger set to true and a RigidBody to collide with each other.

Player should have a RigidBody and a BoxCollider2D component attached to it with the below PlayerPowerUp script attached as well

The power-up should have a BoxCollider2D component attached with Is Trigger set to true with the below TripleShot script attached as well

PlayerPowerUp.cs

using System.Collections;
using UnityEngine;

public class PlayerPowerUp : MonoBehaviour
{
    private bool _hasTripleShot;

    private void Update() {
        if (_hasTripleShot) {
            // Player can do something here
        }
    }

    public void StartTripleShotCountdown() {
        StartCoroutine(TripleShotTimer());
    }

    public IEnumerator TripleShotTimer() {
        Debug.Log("Player has Triple Shot power-up");
        _hasTripleShot = true;
        
        yield return new WaitForSeconds(10f);
        
        _hasTripleShot = false;
        Debug.Log("Player doesn't have Triple Shot power-up anymore");
    } 
}

TripleShot.cs

using UnityEngine;

public class TripleShot : MonoBehaviour
{
    public void OnTriggerEnter2D(Collider2D col)
    {
        if (col.CompareTag("Player")) {
            Debug.Log("Colission is happening");
            SoundManager.instance.Play(SoundManager.SoundName.tripleShotCollect);

            PlayerPowerUp playerPowerUp = col.GetComponent<PlayerPowerUp>();

            if (!playerPowerUp) {
                Debug.LogError("PowerUpScript is not found on player");
            }
            // Call the player's TripleShotTimer CoRoutine
            playerPowerUp.StartTripleShotCountdown();
            Destroy(gameObject);
        }
    }
}

The issue here is you are destroying the gameobject on which you are calling the coroutine.
You can shift the coroutine code to an active gameobject and that can fix your issue