### Tested versions

Godot Engine v4.2.stable.official.46dc27791

### System information

Windows 10

### Issue description

When exporting to web, Godot fails with this error in the console:

> scene/main/window.cpp:884 - Attempting to make child window exclusive, but the parent window already has another exclusive child. This window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->VBoxContainer@<!-- -->137/@<!-- -->AcceptDialog@<!-- -->411, parent window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559, current exclusive child window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->ProgressDialog@<!-- -->17444

![a](https://github.com/godotengine/godot/assets/2000051/bf9d22aa-d3fe-4e11-bff6-c387e740fe90)

This happens for newly created empty projects.


### Steps to reproduce

1. Open the attached project (or create a new project).
2. Project->Export->Export All
3. Observe the console error.  No output files are generated.


### Minimal reproduction project (MRP)

[export_test.zip](https://github.com/godotengine/godot/files/13574810/export_test.zip)

Vector<ExportArchitecture> archs;
	archs.push_back(ExportArchitecture("arm64", true));
	return archs;
}
struct IconInfo {
	const char *preset_key;
	const char *idiom;
	const char *export_name;
	const char *actual_size_side;
	const char *scale;
	const char *unscaled_size;
	const bool force_opaque;
};
static const IconInfo icon_infos[] = {
	
	{ PNAME("icons/iphone_120x120"), "iphone", "Icon-120.png", "120", "2x", "60x60", false },
	{ PNAME("icons/iphone_120x120"), "iphone", "Icon-120.png", "120", "3x", "40x40", false },
	{ PNAME("icons/iphone_180x180"), "iphone", "Icon-180.png", "180", "3x", "60x60", false },
	
	{ PNAME("icons/ipad_76x76"), "ipad", "Icon-76.png", "76", "1x", "76x76", false },
	{ PNAME("icons/ipad_152x152"), "ipad", "Icon-152.png", "152", "2x", "76x76", false },
	{ PNAME("icons/ipad_167x167"), "ipad", "Icon-167.png", "167", "2x", "83.5x83.5", false },
	
	{ PNAME("icons/app_store_1024x1024"), "ios-marketing", "Icon-1024.png", "1024", "1x", "1024x1024", true },
	
	{ PNAME("icons/spotlight_40x40"), "ipad", "Icon-40.png", "40", "1x", "40x40", false },
	{ PNAME("icons/spotlight_80x80"), "iphone", "Icon-80.png", "80", "2x", "40x40", false },
	{ PNAME("icons/spotlight_80x80"), "ipad", "Icon-80.png", "80", "2x", "40x40", false },