Opening window-node makes me lose -10fps in compability mode

### Tested versions

Reproducible in godot 4.0-4.3 dev4

### System information

Windows 11, Compatibility mode

### Issue description

I try to target my game for older devices or laptops without dGPU.

My game opens another window with the window-node (embedded subwindows are off.) Without opening another window the game runs smoothly 60fps. With window the game fps drops to 50fps.

This is without opening window:

And this is with window opened:

The code for the opening window is here:
```
extends Control

const CONTROL_PANEL: PackedScene = preload("res://window.tscn")
func _ready():
var _scene = CONTROL_PANEL.instantiate()

_scene.title = "Control panel"
self.add_child(_scene)
```
Without vsync, my fps is around 1400 but will cause a lot of stuttering (Even if I cap fps to 60.

This is only reproducible in compatibility mode. Forward+ won't make this. I'm running this with intel 12th igpu for testing purposes. Somehow my RTX 3060 can handle the 2 windows.

This problem makes my game not suitable for older laptops even if it's a very simple game.

### Steps to reproduce

Run with igpu and make project compatibility mode.
1. Make the main scene and window scene (Just Godot sprite in both).

Main scene:
```
const CONTROL_PANEL: PackedScene = preload("res://window.tscn")
func _ready():
var _scene = CONTROL_PANEL.instantiate()

_scene.title = "Control panel"
self.add_child(_scene)
```

### Minimal reproduction project (MRP)

[MRP.zip](https://github.com/godotengine/godot/files/14585751/MRP.zip)

Start with the attached MRP and reproduce the frame-rate drop on an Intel 12th-generation iGPU in Compatibility mode when a second window-node is opened. Compare the same project with one window and in Forward+; done means the extra window no longer causes the reported performance loss in Compatibility mode.

Written by the indexing model from the issue text.