Unity C# movement tied to player object

I am toying around with a 2d space shooter. Currently I am trying to fire a projectile forward from the ship (there is a weapon and magazine object but the statement is generally true) and send it hurling into space on its trajectory. The issue is it fires and moves forward but the x axis follow my ship. So I get this strange effect of the bullet going forward but left or right as I move.

My assumption was that when setting the position I was giving it a reference to the ship's position but I tried changing it to a new instance of the vector based on the current position but it still follows my ship. How do I decouple the two objects movement?

public void Shoot()
{
    PlayerWeaponMagazine magazineScript = magazine.GetComponent<PlayerWeaponMagazine>();
    GameObject bullet = magazineScript.UseBullet();
    PlayerWeaponBullet bulletScript = bullet.GetComponent<PlayerWeaponBullet>();
    
    //Relevant Code for spawning the bullet
    var vector3 = new Vector3(gameObject.transform.position.x, gameObject.transform.position.y);
    
    //Assuming this is just a value now and not a reference
    bullet.transform.position = vector3;
    bullet.SetActive(true);
}

Code for the bullet to move:

void Update()
{
    timePassed += Time.deltaTime;
    if (gameObject.activeSelf)
    {
        
        //Relevant code for moving the projectile.
        gameObject.transform.position += ((bulletSpeed * Vector3.up * Time.deltaTime));
        if (timePassed > bulletLifetime)
        {
            gameObject.SetActive(false);
            timePassed = 0f;
        }
    }
}

The UseBullet() is just a pool manager (from comments)

public GameObject UseBullet()
{
    GameObject bullet = pool[poolIndex];
    poolIndex++;
    if (poolIndex > capacity - 1)
    {
        poolIndex = 0;
    }
    return bullet;
}

Adding this for clarity on the answer

void Start()
{
    pool = new GameObject[capacity];
    for (int i = 0; i < capacity; i++)
    {
        GameObject bullet = Instantiate(bulletPrefab);
        bullet.SetActive(false);
        //bullet.transform.SetParent(gameObject.transform);
        pool[i] = bullet;
    }
}

You don't show the code for this call, which is where your issue most likely lies:

magazineScript.UseBullet();

Specifically, from your description, it sounds like you're spawning the bullet as a child of the weapon (or the ship). Being a child, it will inherit (in math terms, multiply) the transform of its parents into its own.

You should be spawning (or even better, reusing) bullets outside of your ship, because once they're spawned they respond to their own physics, not their ship's physics.

Use instantiate for your bullets.

give your bullet a scritp in what you tell it to move in a dicection and a certain speed.

next in the script shoot instantiate the bullet prefab at a starting position (in case of ship or gun, the start possition should be at the end of a gun barrel)
like this:

    // Instantiate at position (0, 0, 0) and zero rotation.
    Instantiate(myPrefab, new Vector3(0, 0, 0), Quaternion.identity);

see the unity documnetation for more info about insantiate and how to use it.
https://docs.unity3d.com/Manual/InstantiatingPrefabs.html