Education question: sync of a variable using Netcode

Hello Dear Unity community

I 'm learning Unity multiplayer and i m stuck with such an initial thing: I can not sync any variable / UI element across 2 players. I spend so much time with no result so now I 'm asking for help.

  1. My Task is to use Relay + Lobby to make 2 players join lobby. For this I use code from Tarodev’s tutorial.
    I made a check button to ‘debug log’ the number of players inside same lobby. After both players ‘joined’ I see ‘2’ as value inside same lobby ID - Success.
  2. Then I want a UI element to share any value among both joined clients: I tried many options. Lets for example use this: 'when I click ‘space’ I want to increase and show value of simple UI element . But when i click ‘Space’ I see Value change only on Host. Also I see that I can not track any events happening on client. Please help me discover the problem and its cause. Without possibility to share any info between clients it is impossible to move for the next step.
    I test it with ParrelSync, FYI
    Also tryed GPT to help me out - he sees no mistakes in my code…

code example of ‘count’:

using UnityEngine;
using UnityEngine.UI;
using Unity.Netcode;
using TMPro;

public class Counter : NetworkBehaviour
{
    private NetworkVariable<int> count = new NetworkVariable<int>(0,NetworkVariableReadPermission.Everyone);

    [SerializeField] private TextMeshProUGUI countText;
    [SerializeField] private TextMeshProUGUI countplayerText;

    private void Update()
    {
        if (Input.GetKeyDown(KeyCode.Space))
        {
            IncrementCountServerRpc();
            Debug.Log(count.Value);
        }

     
    }

  
    private void OnCountChanged(int oldValue, int newValue)
    {
     
        countText.text = newValue.ToString();
    }

    [ServerRpc]
    void IncrementCountServerRpc()
    {
        count.Value++;
    }

    private void OnEnable()
    {
        count.OnValueChanged += OnCountChanged;
    }

    private void OnDisable()
    {
        count.OnValueChanged -= OnCountChanged;
    }

  
}

Use the debugger to see what’s going on at runtime: Unity - Manual: Debug C# code in Unity

The problem is likely with the GameObject that Counter is own. The Counter code seems technically correct.
Does OnNetworkSpawn method get called on the client? If not, it doesn’t exist client-side.