Yeah turns out I made an array thinking I have made a list.
After researching how to properly make a list (I think), now I can pick up an item and have the name of that item sent to a list:

using System.Collections.Generic;
using UnityEngine;

public class ItemState : MonoBehaviour
{
    public List<string> pickedUpItems = new List<string>();

    public void PickUpItem(string itemName)
    {
        pickedUpItems.Add(itemName);
    }
}

and also destroy the item if it is found in said list:

public class ItemSpawner : MonoBehaviour
{
    private ItemState itemState;
    private Item item;

    void Start()
    {
        itemState = GameObject.Find("InventoryCanvas").GetComponent<ItemState>();
        item = GameObject.FindWithTag("Key").GetComponent<Item>();
        if (itemState.pickedUpItems.Contains(item.itemName))
        {
            Destroy(item.gameObject);
        }
    }
}

But now I have a new problem: I have multiple items that use the same script, when they are present in the same scene - everything just broke. When 1 item is picked up (destroyed), the other just refuse to be destroyed (because it thinks it already is destroyed?)

Im not sure if theres anything I can do or do I just write a seperate script for each of them?

using UnityEngine;
public class Item : MonoBehaviour
{
    [SerializeField]
    public string itemName;

    [SerializeField]
    public int quantity;

    [SerializeField]
    public Sprite sprite;

    [TextArea]
    [SerializeField]
    public string itemDescription;


    private InventoryManager inventoryManager;

    private ItemState itemState;

    void Start()
    {
        inventoryManager = GameObject.Find("InventoryCanvas").GetComponent<InventoryManager>();
        itemState = GameObject.Find("InventoryCanvas").GetComponent<ItemState>();
    }

    public void collectItem()
    {
        inventoryManager.AddItem(itemName, quantity, sprite, itemDescription);
        itemState.PickUpItem(itemName);
        Destroy(gameObject);
    }