### 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)

for (size_t i = 0; i < sizeof(icon_size) / sizeof(icon_size[0]); ++i) {
		if (images.has(icon_size[i])) {
			valid_icon_count++;
		} else {
			int size = (icon_size[i] == 0) ? 256 : icon_size[i];
			add_message(EXPORT_MESSAGE_WARNING, TTR("Resources Modification"), vformat(TTR("Icon size \"%d\" is missing."), size));
		}
	}
	ERR_FAIL_COND_V(valid_icon_count == 0, ERR_CANT_OPEN);
	Ref<FileAccess> fw = FileAccess::open(p_dst_path, FileAccess::WRITE, &err);
	if (err != OK) {
		return err;
	}
	
	fw->store_16(0); 
	fw->store_16(1); 
	fw->store_16(valid_icon_count); 
	
	uint32_t img_offset = 6 + 16 * valid_icon_count;
	for (size_t i = 0; i < sizeof(icon_size) / sizeof(icon_size[0]); ++i) {
		if (images.has(icon_size[i])) {
			const IconData &di = images[icon_size[i]];
			fw->store_8(icon_size[i]); 
			fw->store_8(icon_size[i]); 
			fw->store_8(di.pal_colors); 
			fw->store_8(0); 
			fw->store_16(di.planes); 
			fw->store_16(di.bpp); 
			fw->store_32(di.data.size()); 
			fw->store_32(img_offset);