How to register multiple instances "attacking" single enemy?

I recently I tried to write a script in which enemy would be receiving damage by multiple instances.

What baffled me is that the script does not consider other instances damage

I added cooldown, damage and attack speed inside enemy script to speed up the debugging process, but I can't figure out how to register multiple instances attacking at the same time.
do i need to make some kind of a list of "Warriors" that are currently touching the enemy and do a foreach loop?

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

public class HealthSystemScript : MonoBehaviour
{
    
    [SerializeField]
    private int AttackPower;
    public int maxHealth = 100;
    public int currentHealth;
    private float _TimeSinceLastAttack = 10f;
    private float attackCooldown = 5f;

    public HealthBar HealthBar;

    private void Start()
    {
        currentHealth = maxHealth;
        HealthBar.SetMaxHealth(maxHealth);
    }
    
    void Update()
    {
        HealthBar.MaxHealth(currentHealth);
        if (currentHealth <= 0 || Input.GetKey(KeyCode.F))
        {
            Destroy(gameObject);
        }
    }
    
    private void OnCollisionStay2D(Collision2D collision)
    {
        //Check if enemy was hit by Warrior
        if (collision.gameObject.tag == "Warrior" && Time.time > attackCooldown)
        {
            // Abort if we already attacked recently.
            if (Time.time - _TimeSinceLastAttack < attackCooldown) return;
            {
                    //if collided object has "Warrior" Tag then:
                    if (collision.gameObject.CompareTag("Warrior"))
                    {
                        TakeDamage(20);
                        Debug.Log("Boss took 20dmg!");
                        // Remember that we recently attacked.
                        _TimeSinceLastAttack = Time.time;

                                     if (currentHealth <= 0 || Input.GetKey(KeyCode.F))
                                     {
                                            Destroy(gameObject);
                                     }
                    }
            }
        }
    }

    public void TakeDamage(int damage)
    {
        currentHealth -= damage;
        HealthBar.SetHealth(currentHealth);
    }
}

> do i need to make somekind of a list of "Warriors" that are currently touching the enemy and do a foreach loop?

Yes!

OnCollisionStay2D is called for each individual touching collider yes, however, your entire code within it is purely time based!

Since you already re-assign

_TimeSinceLastAttack = Time.time;

for the first touching warrior the other calls to OnCollisionStay2D for the remaining warriors won't pass the

 if (Time.time - _TimeSinceLastAttack < attackCooldown) return;

in that same frame anymore!

If I understood correctly you want to track individual attack times for each warrior so I would rather do something like e.g.

public class HealthSystemScript : MonoBehaviour
{
    [SerializeField]
    private int AttackPower;
    public int maxHealth = 100;
    public int currentHealth;
    public HealthBar HealthBar;

    private float attackCooldown = 5f;

    // maps each attacking warrior to its individual last attack time
    private readonly Dictionary<GameObject, float> _lastAttackTimes = new();

    private void Start()
    {
        currentHealth = maxHealth;
        HealthBar.SetMaxHealth(maxHealth);
    }

    private void OnCollisionStay(Collision2D collision)
    {
        // Check if enemy was hit by Warrior -> no -> ignore
        if (!collision.gameObject.CompareTag("Warrior")) return;

        // This means either this didn't touch before or the previous attack is too recent -> ignore
        if(_lastAttackTimes.TryGetValue(colision.gameObject, out var lastAttackTime) && Time.time - lastAttackTime > attackCooldown) return;
        
        // otherwise inflict damage once now and track last attack time for this warrior
        TakeDamage(20);
        Debug.Log("Boss took 20dmg!");
        _lastAttackTimes[colision.gameObject] = Time.time;
    }

    private void OnCollisionExit2D(Collision2D collision)
    {
        //Check if enemy was hit by Warrior
        if (!collision.gameObject.CompareTag("Warrior")) return;

        // remove from the map of warriors so next first touch is applied immediately
        _lastAttackTimes.Remove(collision.gameObject);
    }

    public void TakeDamage(int damage)
    {
        currentHealth -= damage;

        // by moving this check here you can be sure i is always applied when receiving damage
        // and you don't need to poll check anything each frame
        if (currentHealth <= 0)
        {
            Destroy(gameObject);
        }
        else
        {
            HealthBar.SetHealth(currentHealth);
        }
    }
}

if you rather want to just have one single timer for all warriors combined it gets a bit simpler:

public class HealthSystemScript : MonoBehaviour
{
    [SerializeField]
    private int AttackPower;
    public int maxHealth = 100;
    public int currentHealth;
    public HealthBar HealthBar;

    private float attackCooldown = 5f;

    private int touchingWarriorsAmount;

    private float lastAttackTime;

    private void Start()
    {
        currentHealth = maxHealth;
        HealthBar.SetMaxHealth(maxHealth);
    }

    private void FixedUpdate()
    {
        // run one shared timer for all attacks
        if (Time.time - lastAttackTime > attackCooldown)
        {
            TakeDamage(20 * touchingWarriorsAmount);

            lastAttackTime = Time.time;
        }
    }

    private void OnCollisionEnter2D(Collision2D collision)
    {
        //Check if enemy was hit by Warrior
        if (!collision.gameObject.CompareTag("Warrior")) return;

        // simply increase the counter on enter
        touchingWarriorsAmount++;
    }

    private void OnCollisionExit2D(Collision2D collision)
    {
        //Check if enemy was hit by Warrior
        if (!collision.gameObject.CompareTag("Warrior")) return;

        // simply decrease the counter on exit
        touchingWarriorsAmount--;
    }

    public void TakeDamage(int damage)
    {
        currentHealth -= damage;

        if (currentHealth <= 0)
        {
            Destroy(gameObject);
        }
        else
        {
            HealthBar.SetHealth(currentHealth);
        }
    }
}

if each warrior has different damage power later (just a guess due to the AttackPower) you again might want to use a list and iterate over them of course but still do the time check only once - as said depends on your needs

In general I would rather go the other way round and instead of checking collisions and receive damage I would rather make the attacker the responsible/driving instance and inflict damage on the thing it is colliding with. This way it would be more trivial to have those attack intervals.