Repository: godot
Issue: Node that isn't a tool but was created by tool in editor runs _Process until restart
Labels: bug,topic:editor,topic:dotnet

### Tested versions

v4.3.stable.mono.official [77dcf97d8]

dotnet --info
```
.NET SDK:
 Version:           8.0.402
 Commit:            70aa751718
 Workload version:  8.0.400-manifests.b6724b7a
 MSBuild version:   17.11.4+37eb419ad

Runtime Environment:
 OS Name:     Windows
 OS Version:  10.0.22631
 OS Platform: Windows
 RID:         win-x64
 Base Path:   c:\program files\dotnet\sdk\8.0.402\

.NET workloads installed:
Configured to use loose manifests when installing new manifests.
There are no installed workloads to display.

Host:
  Version:      8.0.8
  Architecture: x64
  Commit:       08338fcaa5

.NET SDKs installed:
  8.0.402 [c:\program files\dotnet\sdk]

.NET runtimes installed:
  Microsoft.AspNetCore.App 8.0.8 [c:\program files\dotnet\shared\Microsoft.AspNetCore.App]
  Microsoft.NETCore.App 3.1.15 [c:\program files\dotnet\shared\Microsoft.NETCore.App]
  Microsoft.NETCore.App 6.0.11 [c:\program files\dotnet\shared\Microsoft.NETCore.App]
  Microsoft.NETCore.App 8.0.2 [c:\program files\dotnet\shared\Microsoft.NETCore.App]
  Microsoft.NETCore.App 8.0.8 [c:\program files\dotnet\shared\Microsoft.NETCore.App]
  Microsoft.WindowsDesktop.App 3.1.15 [c:\program files\dotnet\shared\Microsoft.WindowsDesktop.App]
  Microsoft.WindowsDesktop.App 6.0.11 [c:\program files\dotnet\shared\Microsoft.WindowsDesktop.App]
  Microsoft.WindowsDesktop.App 8.0.2 [c:\program files\dotnet\shared\Microsoft.WindowsDesktop.App]
  Microsoft.WindowsDesktop.App 8.0.8 [c:\program files\dotnet\shared\Microsoft.WindowsDesktop.App]

Other architectures found:
  x86   [C:\Program Files (x86)\dotnet]
    registered at [HKLM\SOFTWARE\dotnet\Setup\InstalledVersions\x86\InstallLocation]

Environment variables:
  Not set

global.json file:
  Not found

Learn more:
  https://aka.ms/dotnet/info

Download .NET:
  https://aka.ms/dotnet/download
```

### System information

Godot v4.3.stable.mono - Windows 10.0.22631 - Vulkan (Forward+) - dedicated NVIDIA GeForce RTX 3070 (NVIDIA; 32.0.15.6094) - AMD Ryzen 9 5950X 16-Core Processor (32 Threads)

### Issue description

When creating a node from a C# tool script, even if the created node is not a tool, it runs its _process function as if it was until the editor is restarted

I may be just misunderstanding how tools work, but I thought that nodes that are not tools should never be able run code in the editor.

### Steps to reproduce

1. Create blank scene
2. Create Tool:
```cs
using Godot;
using System;

[GlobalClass, Tool]
public partial class ThisIsATool : Node3D
{
    [Export] public bool Toggle { 
        get => _toggle;
        set {
            _toggle = value;
            CreateBrokenNode();
        }
    }
    private bool _toggle = false;
    // Called when the node enters the scene tree for the first time.
    public override void _Ready()
    {
    }

    private void CreateBrokenNode()
    {
        var root = EditorInterface.Singleton.GetEditedSceneRoot();
        var node = new ThisIsNotATool();
        AddSibling(node);
        node.SetOwner(root);
    }

    // Called every frame. 'delta' is the elapsed time since the previous frame.
    public override void _Process(double delta)
    {
    }
}
```
3. Create a type that isn't a tool
```cs
using Godot;
using System;

[GlobalClass]
public partial class ThisIsNotATool : Node
{
    // Called when the node enters the scene tree for the first time.
    public override void _Ready()
    {
    }

    // Called every frame. 'delta' is the elapsed time since the previous frame.
    public override void _Process(double delta)
    {
        GD.Print("This is not a tool");
    }
}
```
4. Hitting the toggle will cause node to be created and "This is not a tool" to be spammed in editor.
5. Restart editor, problem goes away.

### Minimal reproduction project (MRP)

[brokentool.zip](https://github.com/user-attachments/files/17439481/brokentool.zip)